Reciprocal graphs
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DOI:
https://doi.org/10.26637/mjm403/005Abstract
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 indexMathematics Subject Classification:
05C10- Pages: 380-387
- Date Published: 01-07-2016
- Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)
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