DM individual assignment

THE MAGAZINE RUNNERS HAVE BEEN WAITING FOR! FIT FOR LIFE ELITE 30 DEC 2021 JOGGING LIFE IN GRAPH EXCLUSIVE! THEORY THE ULTIMATE MOVE FOR POWERFUL LEGS Train smarter Eat healthier Run easier DECEMBER 2021 | $15.98 WWW.ELITERUNNER.COM PREPARE FOR: PROF DR HASLINDA BY: HUE ANN CHEE 285585

CONTENTS JOGGING + FITNESS + FOOD 01 THE STRUCTURE OF TAMAN KSM 02 SADLY RAINING DAY 03 JOGGING + BRISK WALKING 04 ROUND THE \"ISLAND\" TRY JOGGING WHEN 03 FOLLOWING YOUR SEPTEMBER 2015 | ISSUE 05 HEART, IT'S HEALTHIER 619 CEDAR LANE , WEST PALMER, NY 07093 +1-303-777-0202 [email protected] WWW.ELITERUNNER.COM

GOAL MAGAZINE WHY IS JOGGING SO POPULAR? We all know that jogging is a Easy to proceed Many effects on the very popular golden sport. body Many people’s first exercise is For us, jogging is a very jogging, and jogging is also convenient exercise. Help our body fat rate one of the only exercises that Because jogging is decrease, help our bone many athletes do. convenient and you can mineral density increase, do anytime, anywhere, you our body will increase Why is jogging so popular? can jog on a treadmill, you physical strength, help can jog outdoors, you can our mood improve, Because jogging has more also jogging indoors by increase muscle mass, effects on the body, and they stepping in place, so this is improve body and nerve are all positive effects, which a more convenient coordination, etc. If you can bring us good changes. If exercise can bring us good want to get these we jog regularly, we can help changes and help. changes, you must let our body get these changes yourself have jogging training and have a certain exercise frequency.

THE STRUCTURE OF TAMAN KSM

Taman KSM My name is Ann. I was staying at Taman KSM, I will do some jogging with my friend sometime in this Taman. I would like to introduce to you guys the jogging journey with the graph theory. Let's start it. (Google, n.d.)

This is the graph of Taman KSM ADJACENCY LIST In the above was an undirected simple graph for Taman KSM. The vertices were represented as an intersection, while the edges was representing as the path which is road. The adjacency list is one of the methods to represent the graphs. In the adjacency list, we need to list down all the vertices that are adjacent to the vertex. For example, the degree of vertex B is three. It means that vertex B has three adjacent vertices in the graph.

ADJACENCY MATRICES The adjacency matrices in the simple graph have to be symmetric. In the graph, we have 15 vertices. So, the adjacency matrices should be 15 X 15 (Vertex). Same with the adjacency list, find the adjacent vertices for each vertex. Then write “1” for the adjacent vertex. For vertex B in the graph, the vertex has 3 degrees, which means that the vertex should have 3 adjacent vertices which are vertex A, vertex C, and vertex L. If not, just put a “0” for the other vertex.

incidence matrices Incidence matrices is another common way to use to represent the graph. In the graph below is an undirected simple graph that has 15 vertices and 21 edges. In the incidence matrices, the left side is the vertices and the edges are on the above. Different from the adjacency matrices, incidence adjacency needs to find the edges that connect with the adjacent vertex.

ISOMORPHISM It is difficult to determine the Isomorphic must have the different structures of the same number of edges, graph is isomorphic, although because of the one-to-one they have the same number of correspondence between the vertex, same number of edges, set of vertices. and even have the same degree for each vertex. Figure 1 Figure 2 Figure 1, is a part of the graph Taman KSM. Figure 1 and figure 2 both have the same number of vertex and edges. The degree of each vertex is also the same. Figure 2 is isomorphic for figure 1, this is because the vertex for both graphs is a one-to-one correspondence.

SADLY RAINING DAY

The most annoying thing when jogging on rainy days. What’s even more annoying is that it rains halfway through when others are unprepared. What I can do with this situation? Of course, I have to find the shortest path to get home.

G Ann's house was here Ann has enjoyed jogging in the evening. But it is almost rainy and she was the G point there. She has to find the shortest path to go home from G point. Where she should go?

To find the shortest path from the G point, we have to draw a new graph. 4A 4L 7 C K4 4 6 4 4 M3 4B J N1 D O 44 3 8 I 2 P2 3H2 Q E 2F 4 G5 Ann was at the A point now, draw a new graph can find the shortest path easier.

Dijkstra's Shortest Path Algorithm L4 A = 17 4 M 3 N 1 O 3 2 QP

This is the fastest way to let Ann get home.

JOGGING + BRISK WALKING

GOAL MAGAZINE JOGGING + BRISK WALKING ACCELERATES THE BURNING OF BODY FAT Studies have shown that alternately jogging and brisk walking are better for burning fat. Because the movement rate and rhythm changes in the process have stronger stimulation to the muscles and brain, it can exercise muscles and joint reflexes, and can also reduce the risk of regaining weight. Remember to do stretching exercises before and after the exercise to prevent sports injuries. It is also recommended to exercise at least 150 minutes a week.

Always stay at home and make me get fat already. Oh No!!! The orange line represented the route to be jogging by Ann.

I drew the route to be jogging into a graph and show it below. Start from here I will use graph colouring to see whether which road I should jogging and which road I should do the brisk walking.

Graph Colouring for the route map The red dots were represented brisk walking which means that I have to start by brisk walking (M). After that switch to blue dots which is jogging (C) until D point. BRISK WALKING H JOGGING I PF E JO K M D L C

Graph Colouring for whole Taman KSM Using the graph colouring Brisk walking on the whole graph of Taman KSM. We can see Jogging there is three colours of vertices. In addition to Running jogging and brisk walking, we can also run in the Taman. Graph G ������ ( G ) = 3 End This is because there are only three colours of vertices in graph G, which is red, blue, and green. Start

ROUND THE \"ISLAND\"

Although Taman KSM is small, still have its own beauty inside. Walking around the Taman is quite relaxing. Want to jog the whole Taman? Sure, using the spanning tree to help us the least number of paths to go around the whole TAMAN.

Let us start from A point!!!

G E H F D IP O J N END M KC L B START A The result is: A>B>C>D>E>F>G>H>I>J>P >O>N>K>L>M

MINIMUM SPANNING TREE We need to use the weighted graph to find the minimum spanning tree. 2 2 This is my house I use the minimum spanning tree to find the shortest path to my friend's house and go jogging together.

G 4E 4 H 6 F 44 D I 4 P3 4 O1 J N3 2 M2 K QC 3L 4 4 E 2B A5 P3 4 F O1 What is the minimum N3 spanning of the graph? 2M Q 1 (only one) 1+ 2 + (3 X 2) + (4 X 2) 2 (only one) = 17 3 (2) 4 (2) The minimum spanning tree for the graph from my house to my friend's house is 17.

REFLECTION I want to thank Dr Has linda for giving me such a creative thinking assignment. This individual assignment was burning my brain in the beginning, because I don't have any idea and my brain was all about the graph is needed for the network connection. Luckily the idea came when I jogging with my friend one day. The most common way to use the graph for us is to find the shortest path. In conclusion, small graph, but big impact.

REFERENCES Kenneth H.Rosen. (2019). Discrete Mathematics and Its Application. Discrete Mathematics (text book).pdf Sandy Hsu. (2021). Jogging + fast walking is the king?. https://www.elle.com/tw/beauty/health/g3627274 2/slow-run-5-tips/ Google. (n.d).[Google Maps Taman KSM}. Retrieved November 23, 2021, https://www.google.com/maps/place/Taman+Ksm