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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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
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| 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. |
| format | Article |
| id | doaj-art-e7d185056af74f849cc266c9f23aee01 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| 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 |
| record_format | Article |
| 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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