A study of the total chromatic number of equibipartite graphs Original Research Article

The total chromatic number χt(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibipartite graphs of order 2n with maximum degree n − 1. As a part of our results, we disprove the biconformability conjecture.