Distance integral complete r-partite graphs

Ruosong Yang; Ligong Wang

doi:10.2298/FIL1504739Y

Distance integral complete r-partite graphs

Ruosong Yang
, Ligong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let D(G) = (d_ij)_n×n denote the distance matrix of a connected graph G with order n, where d_ij is equal to the distance between vertices v_i and v_i in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In this paper, we investigate distance integral complete r-partite graphs K_p1,p2,...,pr = K_{a1.p1,a2.p2,...,as.ps} and give a sufficient and necessary condition for K_{a1.p1,a2.p2,...,as.ps} to be distance integral, from which we construct infinitely many new classes of distance integral graphs with s = 1,2,3,4.

Original language	English
Pages (from-to)	739-749
Number of pages	11
Journal	Filomat
Volume	29
Issue number	4
DOIs	https://doi.org/10.2298/FIL1504739Y
State	Published - 2015

Keywords

Complete r-partite graph
Distance integral
Distance matrix
Graph spectrum

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10.2298/FIL1504739Y

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title = "Distance integral complete r-partite graphs",

abstract = "Let D(G) = (dij)n×n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vi in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In this paper, we investigate distance integral complete r-partite graphs Kp1,p2,...,pr = Ka1.p1,a2.p2,...,as.ps and give a sufficient and necessary condition for Ka1.p1,a2.p2,...,as.ps to be distance integral, from which we construct infinitely many new classes of distance integral graphs with s = 1,2,3,4.",

keywords = "Complete r-partite graph, Distance integral, Distance matrix, Graph spectrum",

author = "Ruosong Yang and Ligong Wang",

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language = "英语",

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pages = "739--749",

journal = "Filomat",

issn = "0354-5180",

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TY - JOUR

T1 - Distance integral complete r-partite graphs

AU - Yang, Ruosong

AU - Wang, Ligong

PY - 2015

Y1 - 2015

N2 - Let D(G) = (dij)n×n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vi in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In this paper, we investigate distance integral complete r-partite graphs Kp1,p2,...,pr = Ka1.p1,a2.p2,...,as.ps and give a sufficient and necessary condition for Ka1.p1,a2.p2,...,as.ps to be distance integral, from which we construct infinitely many new classes of distance integral graphs with s = 1,2,3,4.

AB - Let D(G) = (dij)n×n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vi in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In this paper, we investigate distance integral complete r-partite graphs Kp1,p2,...,pr = Ka1.p1,a2.p2,...,as.ps and give a sufficient and necessary condition for Ka1.p1,a2.p2,...,as.ps to be distance integral, from which we construct infinitely many new classes of distance integral graphs with s = 1,2,3,4.

KW - Complete r-partite graph

KW - Distance integral

KW - Distance matrix

KW - Graph spectrum

UR - https://www.scopus.com/pages/publications/84929148015

U2 - 10.2298/FIL1504739Y

DO - 10.2298/FIL1504739Y

M3 - 文章

AN - SCOPUS:84929148015

SN - 0354-5180

VL - 29

SP - 739

EP - 749

JO - Filomat

JF - Filomat

IS - 4

ER -

Distance integral complete r-partite graphs

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Keywords

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