ATOM BOND-CONNECTIVITY ENERGY OF A GRAPH

ATOM BOND-CONNECTIVITY ENERGY OF A GRAPH

K. N. Prakasha, P. S. K. Reddy, I. N. Cangul, S. Purushotham

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Abstract

The purpose of this paper is to introduce and investigate the atom bond- connectivity energy ABCE(G) of a graph G. We present some upper and lower bounds for ABCE(G) and calculate it for several graph classes and also for some graphs with one edge deleted which enables us to calculate this index for larger graphs by means of smaller graphs. Also ABCE(G) is calculated for some complements of several graphs..

Keywords

Atom bond-connectivity matrix, atom bond-connectivity energy, atom bond- connectivity characteristic polynomial, k-complement, k(i)-complement.