Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5} and edge-set E = {(1, 2),(3, 2),(4, 3),(1, 4),(2, 4),(1, 3)}. (a) Draw the graph. Find (b) maximal degree, i.e. ∆(G), (c) minimal degree, i.e. δ(G), (d) the size of biggest clique, i.e. ω(G),

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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Question

Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5} and edge-set
E = {(1, 2),(3, 2),(4, 3),(1, 4),(2, 4),(1, 3)}.
(a) Draw the graph.
Find
(b) maximal degree, i.e. ∆(G),
(c) minimal degree, i.e. δ(G),
(d) the size of biggest clique, i.e. ω(G),
(e) the size of biggest independent set, i.e. α(G), ter
(f) the minimal number of colours needed to color the graph, i.e. χ(G).

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5. Let G = (V, E) be a graph with vertex-set V = {1,2,3,4} and edge-set E = {(1, 2), (3, 2), (4, 3), (1, 4), (2,4)}. (a) Draw the graph. Find (b) maximal degree, i.e. A(G), (c) minimal degree, i.e. 8(G), (d) the size of biggest clique, i.e. w(G), (e) the size of biggest independent set, i.e. a(G), ter (f) the minimal number of colours needed to color the graph, i.e. x(G).
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Give an example of two undirected graphs G1 with nodes {f, s, y, r} and G2 with nodes {t, q, n, p, w}, you can choose your own edges as long as you can give a mapping to show the subgraph- isomorphism
G.5
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