Randic Type Additive Connectivity Energy of a Graph

Madhusudhan, K. V. , Reddy, P. S. K. , Rajanna, K. R.
Vladikavkaz Mathematical Journal 2019. Vol. 21. Issue 2.

Abstract:
The Randic type additive connectivity matrix of the graph \(G\) of order \(n\) and size \(m\) is defined as \(RA(G)=(R_{ij})\), where \(R_{ij}=\sqrt{d_{i}}+\sqrt{d_{j}}\) if the vertices \(v_i\) and \(v_j\) are adjacent, and \(R_{ij}=0\) if \(v_i\) and \(v_j\) are not adjacent, where \(d_i\) and \(d_j\) be the degrees of vertices \(v_i\) and \(v_j\) respectively. The purpose of this paper is to introduce and investigate the Randic type additive connectivity energy of a graph. In this paper, we obtain new inequalities involving the Randic type additive connectivity energy and presented upper and lower bounds for the Randic type additive connectivity energy of a graph. We also report results on Randic type additive connectivity energy of generalized complements of a graph.

Keywords: Randic type additive connectivity energy, Randic type additive connectivity eigenvalues

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