Reciprocal graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. A graph G is reciprocal if the reciprocal of each of its eigenvalue is also an eigenvalue of G. The Wiener index $W(G)$ of a graph G is defined by W(G)=1/2 ∑d ∈ D d where D is the distance matrix of G. In this paper some new classes of reciprocal graphs and an upperbound for their energy are discussed. Pairs of equienergetic reciprocal graphs on every n ≡ 0 (12) and n ≡ 0 (16) are constructed. The Wiener indices of some classes of reciprocal graphs are also obtained.