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

数学与统计学院

Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	243-245
页数	3
期刊	Fangzhi Gaoxiao Jichukexue Xuebao
卷	24
期	2
出版状态	已出版 - 6月 2011

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引用此

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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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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

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JF - Fangzhi Gaoxiao Jichukexue Xuebao

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The Laplacian polynomial of complete multipartite graphs

摘要

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