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Total Chromatic Number and Some Topological Indices

Publication Type : Journal Article

Publisher : Electronic Notes in Discrete Mathematics

Authors : Dr. J. Geetha, Dr. Somasundaram K.

Campus : Coimbatore

School : School of Engineering

Department : Mathematics

Year : 2016

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.

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