THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS

The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph  \(G\) with vertex set consisting of \(n\) vertices, is a real symmetric matrix \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) is the distance between the vertices \(v_i\) and \(v_j\) of \(G\) for \(i...

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Bibliographic Details
Main Authors: Ann Susa Thomas, Sunny Joseph Kalayathankal, Joseph Varghese Kureethara
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2021-07-01
Series:Ural Mathematical Journal
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Online Access:https://umjuran.ru/index.php/umj/article/view/285
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Summary:The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph  \(G\) with vertex set consisting of \(n\) vertices, is a real symmetric matrix \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) is the distance between the vertices \(v_i\) and \(v_j\) of \(G\) for \(i \neq j\) and 0 otherwise. The vertex distance complement spectrum of the subdivision vertex join, \(G_1 \dot{\bigvee} G_2\) and the subdivision edge join \(G_1 \underline{\bigvee} G_2\) of regular graphs \(G_1\) and \(G_2\)  in terms of the adjacency spectrum are determined in this paper.
ISSN:2414-3952