Article ID Journal Published Year Pages File Type
5773327 Linear Algebra and its Applications 2017 25 Pages PDF
Abstract
The study of the strong reciprocal eigenvalue property is closely related to the study of graphs which are isomorphic to their inverse graphs. A nonsingular graph G is said to satisfy the property (SR) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and they both have the same multiplicities. In this article, we show that if a unicyclic graph G in H has property (SR), then G is invertible and the inverse graph of G is unicyclic. As an application, we show that a noncorona unicyclic graph in H with property (SR) can have one of the five specified structures. Finally, our discussions lead to the following problem. Does there exist a unicyclic graph G∈H which has property (SR) but G is not self-inverse?
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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