Mathematics Homework Solutions
Problem
#28053

Find a graph G on five vertices such that omega(G) < 3 and omega (G bar) < 3, where "G bar" is the complement of G.

Let G be a graph. Then G = (V, E), where V and E are the vertex set and edge set, respectively, of G.

The clique number of G, omega(G), is the cardinality of the largest subset S of V such that every pair of vertices in S are connected by an edge of G.

The complement of G, which we will refer to as "G bar," is the graph (V, E bar), where V is the vertex set of G bar (i.e., the vertex set of G bar is identical to the vertex set of G) and E bar is the edge set of G bar. The edge set E bar is defined as follows:

For distinct vertices v1, v2, there is an edge that connects v1 and v2 in G bar if and only if there is no edge that connects v1 and v2 in G.

Find a graph G on five vertices such that omega(G) < 3 and omega(G bar) < 3.

Attached file(s):
Attachments
45.8.doc  View File

Attachment Content Summary (Note: view attachment at the above link before purchasing. Actual attachment content may vary slightly from that shown below.)

45.8.doc
INSTRUCTIONS TO OTA

typeset solutions

send solution as attachment

Use words to explain solutions. DO NOT RELY ONLY ON ALGEBRAIC
MANIPULATIONS/ OR SYMBOLS.

Solution Summary

An example of a graph with the specified properties (including a detailed justification) is provided in an attached .doc file.

Solution
What is this?
By OTA - Overall OTA Rating
Purchase Cost Now
$2.19 CAD (was ~$3.99)
Included in Download
  • Plain text response
  • Attached file(s):
    • GraphOn5Vertices-Solution.doc
$2.19 Instant Download
Add to Cart
Why you can trust BrainMass.com
  • Your Information is Secure
  • Best Online Academic Help Service
  • Students find real academic Success
Related Solutions
  • Discrete Math - Please help me with this one! 1. Let G be an undirected graph with n vertices. If G is isomorphic to its own compliment , how many edges must G have?
  • Prove or disprove: If a simple graph with diameter 2 has a cut-vertex, then its edge-complement has an isolated vertex. - Prove or disprove: If a simple graph with diameter 2 has a cut-vertex, (i.e. a vertex whose deletion increases the number of components of G) then its edge-complement has an isolated vertex.
  • Complement Graphs - (1) Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph. (Please read carefully the definition of an induced subgraph bef ...
  • Proving connectedness. - Prove that if G is a disconnected graph, the complement graph G^G is connected, and in fact, diam(G^)<=2.
  • Connected Graphs - Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G? Prove your findings! Let G be a connected graph and sq(G) be a graph which contains ...
Browse