Reciprocal Graphs
Authors :
G. Indulala,* and A.Vijayakumarb
Author Address :
aDepartment of Mathematics, St.Aloysius College, Edathua, Alappuzha - 689573, India.
bDepartment of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India.
*Corresponding author.
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\limits_{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)\text{ 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.
DOI :
Article Info :
Received : November 12, 2015; Accepted : March 25, 2016.
