On Reduced Reciprocal Randic Energy of Tensor product of some graphs

Résumé

Let G = G1 ⊗ G2 be a tensor product of two graphs with m + n vertices
and mn edges. Let V (G) = {wij = (uij , vij) : where 1 ≤ i ≤ m and 1 ≤ j ≤ n}
be the vertex set of G. [4] defined reduced reciprocal randic matrix of a graph
G on n vertices. It is denoted by RRR(G) and it is defined as a n × n matrix
whose (i, j) entry as q (dvi − 1)(dvj − 1) if vi and vj are adjacent. otherwise it is
0. The Reduced reciprocal randic energy RRRE(G) of a graph G is the sum of
the absolute values of the eigenvalues of RRR(G). In this paper, we explore the
reduced reciprocal randic energy RRRE(G) of tensor product RRR(Km ⊗ Kn),
RRR(Km ⊗ Cn), RRR(Cm ⊗ Cn), RRR(Km ⊗ Km,m) and RRRE(K2n ⊗ K2n).