Graph Theory: Handshaking Theorem, Simple Graphs, and Regular Graphs

Math Problem Statement

(ii) State and prove Handshaking theorem. Verify the handshaking theorem for the

following graph. ( Any graph with some vertices and some edges)

(iii) Draw the graphs of C9, W8, K5 and K3,5. How many vertices does a regular graph of

degree 4 and 10 edges?

7b (a) Prove that the maximum number of edges in a simple graph with n vertices is 𝑛(𝑛−1)

(b) Draw the graphs of C10, W9, K6 and K2,5. How many vertices does a regular graph of degree 4

and 10 edges?

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Graph Theory
Degree of Vertices
Regular Graphs
Simple Graphs

Handshaking Lemma: Σ degree of vertices = 2 * number of edges
Maximum edges in a simple graph: n(n-1)/2

Handshaking Theorem

Undergraduate

Finding the Degree of a Vertex in a (7,10) Graph Using Handshaking Lemma

Example of a Regular Graph with 8 Nodes and Degree 3

Maximum Size of Θ-Free Graphs with n Vertices

Determining Impossible Graph Configurations Based on Vertex Degrees

Edge Count in Graph G1,6 Based on Prime Number Sums