REDUCED RECIPROCAL RANDIĆ ENERGY OF A GRAPH
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In this paper, we define reduced reciprocal Randić matrix of a graph G on n vertices. It is denoted by RRR(G) and is defined as an n × n matrix whose (i, j)th entry is √((dᵥᵢ − 1)(dᵥⱼ − 1)) if vᵢ and vⱼ are adjacent, and 0 otherwise. The reduced reciprocal Randić energy is the sum of absolute values of the eigenvalues of RRR(G). Reduced reciprocal Randić energy of some well-known and much studied graphs are reported. Also, an upper and lower bound for the reduced reciprocal Randić energy of a graph with respect to a vertex subset is presented.
Abstract
In this paper, we define reduced reciprocal Randić matrix of a graph G on n vertices. It is denoted by RRR(G) and is defined as an n × n matrix whose (i, j)th entry is √((dᵥᵢ − 1)(dᵥⱼ − 1)) if vᵢ and vⱼ are adjacent, and 0 otherwise. The reduced reciprocal Randić energy is the sum of absolute values of the eigenvalues of RRR(G). Reduced reciprocal Randić energy of some well-known and much studied graphs are reported. Also, an upper and lower bound for the reduced reciprocal Randić energy of a graph with respect to a vertex subset is presented.
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