Discrete Mathem...

Consider a connected graph G in which vertices is equal to the number of edges, and every vertex has degree 2. What is the minimum number of colors required to edge-color G?

A graph G consists of 3 components G₁, G₂ and G₃ with 5, 9 and 13 vertices respectively. Maximum number of edges possible in G is _________.

What is the number of perfect matching in a complete graph K6?

Let G be a graph and G’ be the self-complementing graph if G’ contains 39 edges then the vertices in Graph G is _____.

Which of the following can be degree sequence of simple graph?

I. 2, 3, 3, 3, 3, 3, 4, 5

II. 1, 3, 3, 4, 5, 6, 6

III. 1, 1, 3, 3, 5, 6, 7

An undirected graph G with only one simple path between each pair of vertices has two vertices of degree 4, one vertex of degree 3 and two vertices of degree 2.