Reciprocal graphs

G. Indulal; A.Vijayakumar

doi:10.26637/mjm403/005

Abstract

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 $W(G)=\frac{1}{2} \sum_{d \in D} d$ 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 $n \equiv$ $0 \bmod (12)$ and $n \equiv 0 \bmod (16)$ are constructed. The Wiener indices of some classes of reciprocal graphs are also obtained.

Keywords:

Eigenvalue, Energy, Reciprocal graphs, splitting graph, Wiener index

Mathematics Subject Classification:

05C10

Authors Imprint References Funding Related Articles Downloads

G. Indulal Department of Mathematics, St.Aloysius College, Edathua, Alappuzha - 689573, India.
A.Vijayakumar Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India. https://orcid.org/0000-0002-6673-9751

Pages: 380-387
Date Published: 01-07-2016
Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

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