Seidel Integral Complete r-Partite Graphs

Ligong Wang; Guopeng Zhao; Ke Li

doi:10.1007/s00373-012-1276-6

Seidel Integral Complete r-Partite Graphs

Ligong Wang
, Guopeng Zhao
, Ke Li

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

14 Scopus citations

Abstract

A graph is S-integral (or Seidel integral) if the spectrum of its Seidel matrix consists entirely of integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be S-integral, from which we construct infinitely many new classes of S-integral graphs. We also present an upper bound and a lower bound for the smallest S-eigenvalue (or Seidel eigenvalue) of a complete multipartite graph.

Original language	English
Pages (from-to)	479-493
Number of pages	15
Journal	Graphs and Combinatorics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s00373-012-1276-6
State	Published - Mar 2014

Keywords

Complete r-partite graphs
Graph spectrum
S-integral
Seidel matrix

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10.1007/s00373-012-1276-6

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abstract = "A graph is S-integral (or Seidel integral) if the spectrum of its Seidel matrix consists entirely of integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be S-integral, from which we construct infinitely many new classes of S-integral graphs. We also present an upper bound and a lower bound for the smallest S-eigenvalue (or Seidel eigenvalue) of a complete multipartite graph.",

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author = "Ligong Wang and Guopeng Zhao and Ke Li",

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AU - Zhao, Guopeng

AU - Li, Ke

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AB - A graph is S-integral (or Seidel integral) if the spectrum of its Seidel matrix consists entirely of integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be S-integral, from which we construct infinitely many new classes of S-integral graphs. We also present an upper bound and a lower bound for the smallest S-eigenvalue (or Seidel eigenvalue) of a complete multipartite graph.

KW - Complete r-partite graphs

KW - Graph spectrum

KW - S-integral

KW - Seidel matrix

UR - https://www.scopus.com/pages/publications/84894305825

U2 - 10.1007/s00373-012-1276-6

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M3 - 文章

AN - SCOPUS:84894305825

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EP - 493

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 2

ER -

Seidel Integral Complete r-Partite Graphs

Abstract

Keywords

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