2019/02/06 by R. Rajkumar, Rajkumar, R., M. Gayathri +1
Computer Science · Mathematics · #05C50 #05C76 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1902.02044
openalex publication_date 2019/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we define a ternary graph operation which generalizes the construction of subdivision graph, R-graph, central graph. Also, it generalizes the construction of overlay graph (Marius Somodi et al., 2017), and consequently, Q-graph, total graph, and quasitotal graph. We denote this new graph by [S(G)]H1H2, where G is a graph and, H1 and H2 are suitable graphs corresponding to G. Further, we define several new unary graph operations which becomes particular cases of this construction. We determine the Adjacency and Laplacian spectra of [S(G)]H1H2 for some classes of graphs G, H1 and H2. From these results, we derive the L-spectrum of the graphs obtained by the unary graph operations mentioned above. As applications, these results enable us to compute the number of spanning trees and Kirchhoff index of these graphs.