Publication Type:

Journal Article

Source:

Electronic Notes in Discrete Mathematics, Volume 53, p.363 - 371 (2016)

URL:

//www.sciencedirect.com/science/article/pii/S1571065316300853

Keywords:

Eccentric connectivity index, Geometric arithmetic index, Harmonic index, Randić index, Total Chromatic Number

Abstract:

Abstract The total chromatic number χ ″ ( G ) of G is the smallest number of colors needed to color all elements of G in such a way that no adjacent or incident elements get the same color. The harmonic index H ( G ) of a graph G is defined as the sum of the weights 2 d ( u ) + d ( v ) of all edges uv of G, where d ( u ) denotes the degree of the vertex u in G. In this paper, we show a relation between the total chromatic number and the harmonic index. Also, we give relations between total chromatic number and some topological indices of a graph.

Cite this Research Publication

J. Geetha and Dr. Somasundaram K., “Total Chromatic Number and Some Topological Indices”, Electronic Notes in Discrete Mathematics, vol. 53, pp. 363 - 371, 2016.