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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 10E

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From a graph G = (V, E), with vertices v; E V and edges e; € E, the prism of the graph,
P(G) = (Vp, Ep), is formed as follows:
Let V' be a copy of V with vertices vị, and E' a copy of E with edges e. Now
V, = VUV', and
E, = EU E'U {(vi, v?)|v; E V }.
An example of a graph and its prism is shown below.
(a) If a graph G has n vertices and k edges, find formulae for the number of vertices
and the number of edges in P(G) in terms of n and k.
(b) Explain why none of the following can be the prism of any connected graph:
i. A graph with 9 vertices.
ii. A graph with 10 vertices and 10 edges.
iii. A simple graph with 3 edges.

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