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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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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author Ann Susa Thomas
Sunny Joseph Kalayathankal
Joseph Varghese Kureethara
author_facet Ann Susa Thomas
Sunny Joseph Kalayathankal
Joseph Varghese Kureethara
author_sort Ann Susa Thomas
collection DOAJ
description 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.
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publishDate 2021-07-01
publisher 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
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series Ural Mathematical Journal
spelling doaj-art-e7d185056af74f849cc266c9f23aee012025-08-20T03:19:11ZengUral 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 MechanicsUral Mathematical Journal2414-39522021-07-017110.15826/umj.2021.1.009122THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHSAnn Susa Thomas0Sunny Joseph Kalayathankal1Joseph Varghese Kureethara2Department of Mathematics, St Thomas College, Kozhencherry-689641, KeralaJyothi Engineering College, Cheruthuruthy, Thrissur-679531, KeralaDepartment of Mathematics, Christ University, Bangalore-560029, KarnatakaThe 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.https://umjuran.ru/index.php/umj/article/view/285distance matrix, vertex distance complement spectrum, subdivision vertex join, subdivision edge join
spellingShingle Ann Susa Thomas
Sunny Joseph Kalayathankal
Joseph Varghese Kureethara
THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS
Ural Mathematical Journal
distance matrix, vertex distance complement spectrum, subdivision vertex join, subdivision edge join
title THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS
title_full THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS
title_fullStr THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS
title_full_unstemmed THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS
title_short THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS
title_sort vertex distance complement spectrum of subdivision vertex join and subdivision edge join of two regular graphs
topic distance matrix, vertex distance complement spectrum, subdivision vertex join, subdivision edge join
url https://umjuran.ru/index.php/umj/article/view/285
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