Spectra of R-Vertex Join and R-Edge Join of Two Graphs
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 1
Abstract
The R-graph R(G) of a graph G is the graph obtained from G by introducing a new vertex ue for each e ∈ E(G) and making ue adjacent to both the end vertices of e. In this paper, we determine the adjacency, Laplacian and signless Laplacian spectra of R-vertex join and R-edge join of a connected regular graph with an arbitrary regular graph in terms of their eigenvalues. Moreover, applying these results we construct some non-regular A-cospectral, L-cospectral and Q-cospectral graphs, and find the number of spanning trees.
Authors and Affiliations
Arpita Das, Pratima Panigrahi
Keywords
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- DOI 10.7151/dmgaa.1279
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