Find the chromatic number of each of the graphs given below.(a) The path graph Pn. where n > 2x (Pn) =(b) The cycle graph Cn, where n is evenx(Cn) =(c) The cycle graph Cn, where n is oddx (Cn) =(d) The complete bipartite graph Km,nxX(Km,n) =(e) The complete graph Knx (Kn)

A)the chromatic number of path graph Pn where n>=2 is 2 B)The chromatic number of the cycle Cn…

Answered: Find the chromatic number of each of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Figure 1 below shows three different graphs. The graph in Fig. 1(a) is connected; the graph in Fig. 1(b) is disconnected and has two sections; the graph in Fig. 1(c) is disconnected and has three sections (the isolated vertex G is a section— that’s as small a section as you can get!). Notice that the only difference between the disconnected graph in Fig. 1(b) and the connected graph in Fig. 1(a) is the edge BF. Think of BF as a “bridge” that connects the two sections of the graph in Fig. 1(b). Not surprisingly, we call such an edge a bridge. A bridge in a connected graph is an edge that keeps the graph connected—if the bridge were not there, the graph would be disconnected. The graph in Fig. 1(a) has three bridges: BF, FG, and FH Draw the graphs for item (c)and then, list all the bridges in each of the three graphs graphs: c) the graph with vertex set {A, B, C, D, E} and edge list AB, BC, CD, DE
What kind of symmetry do the following graphs have, if any? y (3) (4) (5) (6)
2. Answer the following questions for the graph below. T4 (a) What are the order and size of this graph? (b) Is this graph a path? If yes, re-draw the graph so that it is clear that it is the graph of a path. If no, then explain why. (c) Is this graph a cycle? If yes, re-draw the graph so that it is clear that it is the graph of a cycle. If no, then explain why.
I am keeping getting different answer. Please answer the question only if you know the answer!
H V Y Consider the graph given above. Add an edge so the resulting graph has an Euler path (without repeating an existing edge). Now give an Euler path through the graph with this new edge by listing the vertices in the order visited.
Let G be the following graph. Do not have to show an explanation for your answers in this problem. (g) Find the edge connectivity.(h) Find the degree sequence.(i) Is this graph a Hamiltonian graph?
Which of the following is the adjacency ma- trix of the given graph? 1 4 3 1 2 1 2 2 0 1 2 1 1 1 0 1 2 1 2 2 0 1 1 1 1 1 1 1 2 0 2 0 1 1 1 1 1 1 1 1 1 0 1 10 1 10 1 0] 2.
Question 11 Consider the graph G in the diagram below. Graph G What are the edge and vertex connectivity of G? The edge and vertex connectivity are both equal to 3. None of the other responses is correct. The edge connectivity is 4 and the vertex connectivity is 3. The edge and vertex connectivity are both equal to 4.
How to make graphs
Solve question no 7 only early
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-17-16 -15 -14 -13 -12 -11 -10 -9--8--7 -5 Submit Question to Find an equation for the graph above. kn 3+p(v) 1 w 3₂ ✔ 9 10 11 o

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Find the chromatic number of each of the graphs given below. (a) The path graph Pn. where n > 2 x (Pn) = (b) The cycle graph Cn, where n is even x (Cn) = (c) The cycle graph Cn, where n is odd x (Cn) = (d) The complete bipartite graph Km,n x X (Km,n) = (e) The complete graph Kn x (Kn)