Degree Subtraction Adjacency Eigenvalues and Energy of Graphs Obtained From Regular Graphs
ODAM-Vol. 1 (2018), Issue 1, pp. 08–15 | Open Access Full-Text PDF
Harishchandra S. Ramane, Hemaraddi N. Maraddi
Abstract:Let \(V(G) = \{v_1, v_2, \ldots, v_n\}\) be the vertex set of \(G\) and let \(d_{G}(v_i)\) be the degree of a vertex \(v_i\) in \(G\). The degree subtraction adjacency matrix of \(G\) is a square matrix \(DSA(G)=[d_{ij}]\), in which \(d_{ij}=d_{G}(v_i)-d_{G}(v_j)\), if \(v_i\) is adjacent to \(v_j\) and \(d_{ij}=0\), otherwise. In this paper we express the eigenvalues of the degree subtraction adjacency matrix of subdivision graph, semitotal point graph, semitotal line graph and total graph of a regular graph in terms of the adjacency eigenvalues of \(G\). Further we obtain the degree subtraction adjacency energy of these graphs.