To cement the question, consider a simple example: a graph with three connected vertices in the shape of a triangle. You can isolate any two vertices and see that they share an odd number of ...

This dooms our party game to failure. Think about the graph we’d like to construct to win the game: It must have seven people and seven odd degrees. Now let’s find the degree sum: Add the first two ...

Amy Dykstra, Michelle Schultz, A GENERALIZATION OF ODD AND EVEN VERTICES IN GRAPHS, Pi Mu Epsilon Journal, Vol. 9, No. 2 (SPRING 1990), pp. 73-79 ...

Abstract Let Kn be a complete graph with n vertices, Ck denote a cycle of length k, and Sk denote a star with k edges. If k = 3, then we call C3 a triangle and S3 a claw. In this paper, we show that ...

These methods involve assigning numerical labels to the vertices and edges of a graph to generate unique weight sums, thereby distinguishing each element’s role within the structure.

This conjectured value for the crossing number of K m,n can be realized by the following drawing. Place n/ 2 vertices on the positive x-axis and n/ 2 vertices on the negative x-axis (or (n +1)/2 and ...