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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa685ae43-1077-4196-9945-72cac3641a58%2F956cc6bf-5cb0-4957-b9a9-72a6fdadb099%2Fpqzcufb_processed.png&w=3840&q=75)
Transcribed Image Text: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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