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Czechoslovak Mathematical Journal

, Volume 66, Issue 2, pp 457–464 | Cite as

Remarks on D-integral complete multipartite graphs

  • Pavel Híc
  • Milan Pokorný
Article
  • 40 Downloads

Abstract

A graph is called distance integral (or D-integral) if all eigenvalues of its distance matrix are integers. In their study of D-integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on D-integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs \({K_{{p_1},{p_2},{p_3}}}\) with p 1 < p 2 < p 3, and \({K_{{p_1},{p_2},{p_3},{p_4}}}\) with p 1 < p 2 < p 3 < p 4, as well as the infinite classes of distance integral complete multipartite graphs \({K_{{a_1}{p_1},{a_2}{p_2},...,{a_s}{p_s}}}\) with s = 5, 6.

Keywords

distance spectrum integral graph distance integral graph complete multipartite graph 

MSC 2010

05C50 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Faculty of EducationTrnava UniversityTrnavaSlovakia

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