What do the in-degree and the out-degree of a vertex in adirected graph modeling a round-robin tournament represent?

In a high school class, there are students of different talents (ex. music, art, debate, sports, etc.). A committee needs to be formed consisting of the maximum number of students such that the committee is diverse – no two students with the same talent are in the committee. Transform this problem to a graph theoretic problem. What are the vertices of the graph? What are the edges of the graph? What do you have to find in the graph?

Either draw the graph that meets the conditions below or explain why no such graph exists: A 9 vertex connected graph with no loops and no multiple edges with exactly 12 edges and three cycles.

What is the minimum number of colors you need to color the vertices of this graph such that if two vertices are adjacent they receive different colors?

in a graph What is the block-cutpoint graph of a graph ? And give example an

Discrete Math

(a) Draw a simple graph (no loops or multiple edges) with vertex degrees 3,3,3,3,4,4,4,6. (b) How many edges does its complement have? Explain.

Find a self-complementary graph with 8 vertices.