Remarks on $D$-integral complete multipartite graphs

Híc, Pavel; Pokorný, Milan

doi:10.1007/s10587-016-0268-8

Geodesic

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Remarks on

D

-integral complete multipartite graphs

Híc, Pavel ; Pokorný, Milan

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 457-464.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

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}

, and

K_{p_{1}, p_{2}, p_{3}, p_{4}}

with

p_{1}

, as well as the infinite classes of distance integral complete multipartite graphs

K_{a_{1} p_{1}, a_{2} p_{2}, \dots, a_{s} p_{s}}

with

s = 5, 6

MR Zbl

DOI : 10.1007/s10587-016-0268-8

Classification : 05C50
Mots-clés : distance spectrum; integral graph; distance integral graph; complete multipartite graph

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     title = {Remarks on $D$-integral complete multipartite graphs},
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Híc, Pavel; Pokorný, Milan. Remarks on $D$-integral complete multipartite graphs. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 457-464. doi : 10.1007/s10587-016-0268-8. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0268-8/

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