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

Ann Susa Thomas     (Department of Mathematics, St Thomas College, Kozhencherry-689641, Kerala, India)
Sunny Joseph Kalayathankal     (Jyothi Engineering College, Cheruthuruthy, Thrissur-679531, Kerala, India)
Joseph Varghese Kureethara     (Department of Mathematics, Christ University, Bangalore-560029, Karnataka, India)

Abstract


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.

Keywords


Distance matrix, Vertex distance complement spectrum, Subdivision vertex join, Subdivision edge join

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References


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DOI: http://dx.doi.org/10.15826/umj.2021.1.009

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