The Laplacian polynomial of complete multipartite graphs

Guo Peng Zhao; Li Gong Wang

The Laplacian polynomial of complete multipartite graphs

Guo Peng Zhao
, Li Gong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

2 Scopus citations

Abstract

The existence problem of Laplacian integral graphs is studied. Let A(G) denotes the adjacency matrix of graph G with n vertices and D(G) denotes the degree diagonal matrix of graph G. The Laplacian matrix of graph G is L(G) =D(G)-A(G). By studying the Laplacian characteristic polynomial of the complete multipartite graph K_{p1, p2⋯ pr'} it is obtained that all the complete multipartite graphs K_p1.P2⋯,Pr are Laplacian integral.

Original language	English
Pages (from-to)	243-245
Number of pages	3
Journal	Fangzhi Gaoxiao Jichukexue Xuebao
Volume	24
Issue number	2
State	Published - Jun 2011

Keywords

Complete multipartite graph
Laplacian integral
Laplacian polynomial

Cite this

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title = "The Laplacian polynomial of complete multipartite graphs",

abstract = "The existence problem of Laplacian integral graphs is studied. Let A(G) denotes the adjacency matrix of graph G with n vertices and D(G) denotes the degree diagonal matrix of graph G. The Laplacian matrix of graph G is L(G) =D(G)-A(G). By studying the Laplacian characteristic polynomial of the complete multipartite graph Kp1, p2⋯ pr' it is obtained that all the complete multipartite graphs Kp1.P2⋯,Pr are Laplacian integral.",

keywords = "Complete multipartite graph, Laplacian integral, Laplacian polynomial",

author = "Zhao, \{Guo Peng\} and Wang, \{Li Gong\}",

year = "2011",

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issn = "1006-8341",

publisher = "Xi'an Polytechnic University",

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T1 - The Laplacian polynomial of complete multipartite graphs

AU - Zhao, Guo Peng

AU - Wang, Li Gong

PY - 2011/6

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N2 - The existence problem of Laplacian integral graphs is studied. Let A(G) denotes the adjacency matrix of graph G with n vertices and D(G) denotes the degree diagonal matrix of graph G. The Laplacian matrix of graph G is L(G) =D(G)-A(G). By studying the Laplacian characteristic polynomial of the complete multipartite graph Kp1, p2⋯ pr' it is obtained that all the complete multipartite graphs Kp1.P2⋯,Pr are Laplacian integral.

AB - The existence problem of Laplacian integral graphs is studied. Let A(G) denotes the adjacency matrix of graph G with n vertices and D(G) denotes the degree diagonal matrix of graph G. The Laplacian matrix of graph G is L(G) =D(G)-A(G). By studying the Laplacian characteristic polynomial of the complete multipartite graph Kp1, p2⋯ pr' it is obtained that all the complete multipartite graphs Kp1.P2⋯,Pr are Laplacian integral.

KW - Complete multipartite graph

KW - Laplacian integral

KW - Laplacian polynomial

UR - https://www.scopus.com/pages/publications/84873037880

M3 - 文章

AN - SCOPUS:84873037880

SN - 1006-8341

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JO - Fangzhi Gaoxiao Jichukexue Xuebao

JF - Fangzhi Gaoxiao Jichukexue Xuebao

IS - 2

ER -

The Laplacian polynomial of complete multipartite graphs

Abstract

Keywords

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