The following questions are mostly on the topic of vertex degrees. (a) Let H be a (8, 13)-graph with 8(H) = 2 and A(H) = 4. Denote by ni the number of vertices in H of degree i, where i = 2,3,4. Assume that n3 ≥ 1. Find all possible answers for (n2, n3, n4). For each of your answers, construct a corresponding graph. (b) Suppose G is a k-regular (n, m )-graph, where k > 0, m ≥ 0 and n ≥ 1. Find a relation linking k, n and m. Justify your answer. (c) Let G be a 3-regular graph with e(G) = 2v(G) – 3. Determine the values of v(G) and e(G). Construct all such graphs G. (d) Let G be a graph of order n in which there exists no three vertices u, v, w such that uv, vw and wu are all edges in G. Show that n≥ 8(G) + A(G).

The following questions are mostly on the topic of vertex degrees. (a) Let H be a (8, 13)-graph with 8(H) = 2 and A(H) = 4. Denote by ni the number of vertices in H of degree i, where i = 2,3,4. Assume that n3 ≥ 1. Find all possible answers for (n2, n3, n4). For each of your answers, construct a corresponding graph. (b) Suppose G is a k-regular (n, m )-graph, where k > 0, m ≥ 0 and n ≥ 1. Find a relation linking k, n and m. Justify your answer. (c) Let G be a 3-regular graph with e(G) = 2v(G) – 3. Determine the values of v(G) and e(G). Construct all such graphs G. (d) Let G be a graph of order n in which there exists no three vertices u, v, w such that uv, vw and wu are all edges in G. Show that n≥ 8(G) + A(G).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.3: Logarithmic Functions And Their Graphs

Problem 137E

See similar textbooks

Similar questions

a If a graph is symmetric with respect to the x-axis and (a,b) is on the graph, then (,) is also on the graph. b If a graph is symmetric with respect to the y-axis and (a,b) is on the graph, then (,) is also on the graph. c If a graph is symmetric about the origin and (a,b) is on the graph, then (,) is also on the graph.
Use symmetry to sketch the graph of xy2=1.

Recommended textbooks for you

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning