NCRIS Abstract Book

MT001-Longitudinally Rough Short Bearing Mital Patel Department of Mathematics, M. K. Bhavnagar University, Bhavnagar, Gujarat, India Email: [email protected] ATTEMPT HAS BEEN TO STUDY AND ANALYSE the performance of short bearing under thepresence of magnetic fluid as a lubricant. Bearing surfaces are considered to be longitudinallyrough. The roughness is characterized by a stochastic random variable with non-zero mean,variance and skew-ness. The modified Reynolds’ equation is solved with suitable boundaryconditions to obtain the pressure distribution. This expression for pressure distribution is usedto calculate the load carrying capacity. Numerical integration is calculated by Simpson’s 1/3rule. The results are presented graphically. It is seen that due to magnetization theperformance of bearing system gets improvement. It is also observed that the effect ofroughness is negative on the performance of the bearing. The investigation suggests that thenegative effect of roughness can be reduced by positive effect of magnetization parameter. Itis also observed that the performance gets improve in the case of suitable combination ofroughness parameters. MT002-Dominator Coloring of Some New Graphs Dr. Minal S. Shukla Atmiya Institute of Technology and Science, Rajkot-360005, Gujarat, India Email: [email protected] graph has a dominator coloring if it has a proper coloring in which each vertex of the graphdominates every vertex of some color class. The dominator chromatic number  G is the dminimum number of color classes in a dominator coloring of a graph G. The open problemswere raised by Gera [1]: Are there any graphs for which  G   G   G and d G   G  G 1holds? We have found an affirmative answer in this regard. We dinvestigate some graphs for which above two conditions hold.Keywords: coloring, domination number, dominator coloring 151

MT003-A Study of Some Results on a Unit Disk Jekil Gadhiya V.V.P Engineering College, Rajkot 360 005, Gujarat, India Email: [email protected] this article we study some important results of the complex analysis. Particularly we studyall the results on a unit disk. Also we give another proof of some well-known theorem.MT004-Some Results on a Spanning Subgraph of the Intersection Graph of Ideals of a Commutative Ring Pravin B. Vadhel Department of Applied Science and Humanities, V.V.P. Engg. College, Rajkot, Gujarat, India Email: [email protected] rings considered in this article are commutative with identity and whichadmit at least onenonzero proper ideal. For a ring , we denote by ( ), the set of all proper ideals of and let ( )∗ = ( )\{(0)}. In this article, for any ring , we associate an undirected simple graph,denoted by ( ), whose vertex set is ( )∗ and distinct vertices , are joined by an edge inthis graph if and only if ≠ (0). For a ring , we determine necessary and sufficientconditions in order that ( ) is connected and also find its diameter when it is connected.We prove that girth ( ( )) is either equal to 3 or 1. Moreover, we classify the rings R forwhich girth ( ( )) = 3. Furthermore, we determine necessary and sufficient conditions inorder that ( ) is complemented.Keywords: B-prime of (0), diameter, girth, complemented graph. MT005-Some Remarks on the Complement of a Comaximal Graph of a Commutative Ring Jaydeep Parejiya Department of Mathematics, Government Polytechnic, Rajkot, Gujarat, India Email: [email protected] 152

Let R be a commutative ring with identity 1 ≠ 0. In this article we study the complement ofa com aximal graph( ( )) , whose vertex set is the set of all nonunits of which are not inJacobson radical ( ) of and two distinct vertices , are adjacent in ( ( )) if and onlyif + ≠ . In this article we prove some important results of a ring using this graphand also prove some important results of this graph. MT006- Mathematics for the Aviation: Major Controlling Parameters of the Aircraft and Flight Gandhi Srushti Alkeshkumar Department of Mathematics, M.K.B.University, Bhavnagar, Gujarat, India Emaul: [email protected] current presentation deals with the specific aspects of the work that an aviation machinemay encounter. The weight of an aircraft is discussed by calculating its wing area, aspectratio, wing loading etc. Also, the mathematics related to some other important structural partsof the aircraft like the thickness of airfoils, wing-rib, nosepiece, tail section, the upper andlower chamberetc is briefly discussed here.Keywords: The weight of aircraft, calculating wind area, wing rib, airfoils MT007-Minimal Roman Dominating Functions Kalariya, K.N. V.V.P. Engineering College, Rajkot, Gujarat, India Email: [email protected] this paper the concept of Minimal Roman dominating function is considered. We provethat a necessary and sufficient condition under which dominating function become minimaldominating function. We also prove that If : ( )  {0,1} is a minimal dominatingfunction then = 2 is a Minimal Roman dominating function. A characterization of aMinimal Roman dominating function has been proved. It is also true that if is a MinimalRoman dominating function then 2 − is a Roman dominating function for a graph withoutisolated vertices. 153

MT008-Fixed Point Theorem in Fuzzy Metric Space 1Preeti Malviya, 2Vandana Gupta, 3Badshah, V.H. and 4Arihant Jain 1Government New Science College, Dewas, Madhya Pradesh, India 2Government Kalidas Girls PG College, Ujjain, Madhya Pradesh, India 3School of Studies in Mathematics, Vikram University, Ujjain, Madhya Pradesh, India 4Shri Guru Sandipani Institute of Technology and Science, Ujjain, Madhya Pradesh, India Email: mpreeti2709@ gmail.comABSTRACTThe purpose of this paper is to prove some new common fixed point theorem in fuzzy metricspace, while proving our result, we utilize the idea of Occasionally weakly compatiblemapping together with Reciprocal continuity due to R.P. Pant and R.K.Bisht. Our resultextended and generalized the result of Som.Keywords: Fuzzy metric space, Reciprocal continuous mapping, Semi-compatible mapping,occasionally weakly compatible mapping. MT009-Semi Continuity Jadav Nilamben Dansangbhai Department of Mathematics, M.K.B. University, Bhavnagar, Gujarat Email: [email protected] presentation deals with the function which is weaker than the continuous function i.e.semi continuous function. The discussion will be done about its types, its examples,properties and its application in this presentation.Keywords: Semi continuous function, properties, continuous function. MT010-Edge-Vertex Domination in Graphs Neha P. Jamvecha and Thakkar, D.K. Department of Mathematics, Saurashtra University, Rajkot-360005, Gujarat, India Email: [email protected] this paper we continue the study of ev-domination (edge-vertex domination) in graphs. Wegive a characterization of minimal ev-dominating sets in graphs. In particular we prove thatin a graph with minimum vertex degree greater than or equal to 2, the complement of a 154

minimal ev-dominating set is an edge dominating set. We also state and prove necessary andsufficient condition under which the ev-domination number increases or decreases when avertex is removed from the graph. We also consider the operation of removing an edge fromthe graph and prove that the ev-domination number does not decrease when an edge isremoved from the graph.Keywords: ev-dominating set, minimal ev-dominating set, minimum ev-dominating set, ev-domination number, edge dominating set, private vertex neighbourhood of an edge MT011-About Isolate Inclusive Sets in Graphs 1Savaliya, N.J. and 2Thakkar, D.K. Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India Email: [email protected] this paper we further study isolate domination in graphs. In particular we study the effectof removing an edge from the graph on the isolate domination number of the graph. Weprove a necessary and sufficient condition under which the isolate domination numberincreases when an edge is removing from the graph. Further we also prove a necessary andsufficient condition under which the isoinc number increases when an edge is removing fromthe graph. We also consider the graphs for which isolate dominating number is equal to 2.Keywords: isolate dominating set, minimal isolate dominating set, minimum isolatedominating set, isolate domination number, isolate inclusive set, private neighborhood MT012-Fractional Domination in Graphs Badiyani, S.M. Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India Email: [email protected] this paper we consider the effect of removing a vertex from a graph G on the FractionalDomination Number of the graph. In particular we prove a necessary and sufficient conditionunder which the Fractional Domination Number of the given graph increases. We also provethat if the Fractional Domination Number decreases then it decreases by atmost 1.Keywords: Fractional Dominating Function, Minimal Fractional Dominating Function,Minimum Fractional Dominating Function, Fractional Domination Number. 155

MT013-Path Union and Cycle of Graphs with Mean Labelling Makadia, H.M. Lukhdhirji Engineering College, Morbi, Gujarat, India Email: [email protected] this presentation we discussed about the mean labeling for path union of various graphslike , , , × , . Also we discussed about the mean labeling for cycle of , , × . Path union of any mean graphs is mean graph for that we recall Step gridgraph is mean graph.Keywords: Cycle, Complete bipartite graph, Grid graph, Step grid graph, Path union ofgraphs, Cycle of graphs and Mean labeling MT014-Geometric Mean 3−Equitable Labeling of some Graphs 1Meera Meghpara, 2Kaneria, V.J. and 3Maulik Khoda 1Department of Mathematics, RK University, Rajkot, Gujarat, India 2Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India 3V.V.P. Engineering College, Rajkot, Gujarat, India Email: [email protected] this paper we proved that K , (m, n ≥ 4) is not a geometric mean 3−equitable graph,while caterpillar S(x , x , … , x ), C ⊙ tK (t ≥ 2) both are geometricmean 3−equitablegraphs. We also proved that C ⊙ K is not geometric mean 3−equitable graph, whenn ≡ 0 ( mod 3 ), while it is geometric mean 3−equitable graph, when n ≡ 1, 2 ( mod 3 ).MT015-Study of Different Graphs with Absolute Mean Graceful Labelling Hiren P. Chudasama Government Polytechnic, Rajkot, Gujarat, India Email: [email protected] the present study of paper, we defined absolute mean graceful labeling for various graphs.We proved all path graphs , cycle , complete bipartite graph , , grid graph × ,step grid graph and double step grid graph are absolute mean graceful graphs.Keywords: Absolute mean graceful labeling. 156

MT016-Balanced Z4-Cordial Graph and its Application to Produce New Balanced Z 4-Cordial Families 1Jaydev Teraiya and 2Kaneria, V.J. 1Marwadi University, Rajkot, Gujarat, India 2Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India Email: [email protected] this paper we discussed about balanced Z4-cordial labeling. We proved that C8t, star ofC8t, Pn*C8t, P (n. C8t),where n ≡ 1 (mod 8), C (n. C8t),where n ≡0 (mod 4) are balanced Z4-cordial graphs.Also we proved that the corona graph of C8tand C8r where r, t € N, is balancedZ4 -cordial graph whenC8t and C8r both are balanced Z4 -cordial.Keywords: Z4-cordial labeling, Balanced Z4-cordial labeling, Star of graph G, Complete starof graph G, Corona graph MT017-Even Sum Labeling of Some Graphs Pritesh Andharia and Kaneria, V.J. Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India Email: [email protected] ( , ) graph = ( , ) is said to be even sum graph if there exists an injective function : ( ) → {0, ±2, ±4, … … , ±2 } such that the induced mapping ∗: ( ) → {2,4, … … , 2 }defined by ∗( ) = ( ) + ( ), ∀ ∈ ( ) is bijective. The function is called an evensum labeling of . In this paper we investigate even sum labeling of some graphs.Keywords: even sum graph, even sum labeling. MT018-Snakes Related Strongly*Graphs 1Jadav, I.I. and 2Ghodasara, G.V. 1Department of Mathematics, RK University, Rajkot, Gujarat, India 2H. & H. B. Kotak Institute of Science, Rajkot, Gujarat, India Email: [email protected] graph with n vertices is said to be strongly*graph if its vertices can be assigned the values{1,2,..., n } in such a way that when an edge whose end vertices are labelled i and j, is 157

labelled with the value (i+j+ij) such that all edges have distinct labels. Here we derive somesnakes related strongly*graphs.Keywords: Strongly*labeling, Strongly*graph MT019-Convergence of Homotopy Analysis Method about the Fractional KDV Partial Differential Equations Gohil, V.P. and Meher, R.K. Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat, India Email: [email protected] In this paper, we obtain the solution of Fractional KDV partial differential equations byusing the homotopy analysis method. The convergence of the homotopy analysis methodabout the considered fractional KDV partial differential equation is also checked.Keywords: Homotopy analysis method, PDE, Fractional derivative, Convergence, KDVequation MT020-Comparison Study of Differential Transform Method with Homotopy Asymptotic Method for Jeffery Hamel flow 1Patel, N.D. and 2Ramakanta Meher 1Mathematics Department, Government Engineering College, Gandhinagar, Gujarat, India 2Department of Mathematics, S.V. National Institute of Technology, Surat, Gujarat, India Email: [email protected] present article discusses the solution of governing equation which is arises during fluidflow between two rigid plane walls. This type of flow is known as a Jeffery Hamel flow & 2αis angle between walls. Differential Transform method (DTM) is demonstrated to obtainsolution for the governing equation. The validity of the differential transform method isascertained by comparing obtained results with homotopy asymptotic method and numerical(Runge Kutta method) results. The effects of the taking different values of Reynolds number(Re) and the angle between the two walls are shown and discussed in the proposed work. Theresults conclude that the proposed analytical method can achieve good agreement inpredicting the solutions of such problems. 158

Keywords: Jeffery-Hamel flow, Differential Transform Method, Nonlinear DifferentialEquation. MT021-Difference Cordial of Operational Graph Related to Cycle 1Vaghasiya, S.M. and 2Ghodasara, G.V. 1RK University, Rajkot, Gujarat, India 2H. & H. B. Kotak Institute of Science, Rajkot, Gujarat, India Email: [email protected] G be a (p; q) graph. A bijective vertex labelling function f : V (G)→{1, 2, ………,p} iscalled a difference cordial labelling if for each edge uv, assign the label |f(u) - f(v)| then |ef(0)- ef(1)| ≤ 1, where ef(1) and ef(0) denote the number of edges labelled with 1 and not labelledwith 1 respectively. A graph with a difference cordial labelling is called a difference cordialgraph. In this paper, we prove that cycle with one chord, cycle with twin chords, cycle withtriangle and swastik graph admit difference cordial labelling.Keywords: Difference cordial, Cycle with one chord, Cycle with twin chord, Cycle withtriangle, Swastik graph MT022-Difference Cordial Labeling in context of Vertex Switching and Ring Sum of Graphs 1Nidhi M. Parsania and 2Rokad, A.H. 1Department of Applied Science & Humanities, VVP Engineering College, Rajkot, Gujarat 2Department of Mathematics, School of Engineering, RK University, Rajkot, Gujarat Email: [email protected], [email protected] G be a (p, q) graphs. Let f: V (G) →{1, 2,..., p} be a function. For each edge uv, assignthe label |f(u) – f(v)|. F is called difference cordial labeling if f is a one to one map and |ef(0)– ef(1)| ≤ 1, where ef(1) and ef(0) denote the number of edges with labeled 1 not labeled with1 respectively. A graph with a difference cordial labeling is called a difference cordial graph. In this paper we prove that vertex switching of cycle, cycle with one chord, cycle withtwin chords and path graphs are difference cordial. Moreover, we prove that cycle ring sumstar graph, cycle with one chord ring sum star graph, gear ring sum star graph and path graphring sum star graph are difference cordial.Keywords: Difference cordial labeling, Vertex switching and Ring sum 159

MT023-Result on Unique Common Fixed Point of Two Continuous Mapping Ashishkumar K. Dhokiya Sardar Patel College of Engineering, Vadtal-Bakrol Road, Bakrol-388 315, Anand, Gujarat Email: [email protected] this paper, generalization of common fixed point is proved under a generalized inequalityinvolving two self-mappings. In other words Let be a closed subspace of a Hilbert Spaceand , ∶ → be continuous mappings satisfying the given condition thenhave unique common fixed point in .Keywords: Common Fixed Point, Banach Space, Completeness 160