Vol. 69, No. 1, pp. 53–64 (2017)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


Some constructions of graphs with integral spectrum

B. R. Rakshith

Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru - 570 006, India E-mail: ranmsc08@yahoo.co.in

Abstract: A graph G is said to be an integral graph if all the eigenvalues of the adjacency matrix of G are integers. A natural question to ask is which graphs are integral. In general, characterizing integral graphs seems to be a difficult task. In this paper, we define some graph operations on ordered triple of graphs. We compute their spectrum and, as an application, we give some new methods to construct infinite families of integral graphs starting with either an arbitrary integral graph or integral regular graph. Also, we present some new infinite families of integral graphs by applying our graph operations to some standard graphs like complete graphs, complete bipartite graphs etc.

Keywords: Integral graphs; Kronecker product.

Classification (MSC2000): 05C50

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 29 Dec 2016. This page was last modified: 10 Jan 2017.

© 2016 Mathematical Society of Serbia (Društvo matematičara Srbije)
© 2016–2017 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition