Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651555 | Electronic Notes in Discrete Mathematics | 2016 | 9 Pages |
Abstract
The total chromatic number χ″(G)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)H(G) of a graph G is defined as the sum of the weights 2d(u)+d(v) of all edges uv of G , where d(u)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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
J. Geetha, K. Somasundaram,