Abstract
Given a graph \(G_1\), the vertex-corona (corona) and the edge-corona focus only on vertices and edges respectively, in forming the corona product with other graphs. In the present work, we define a new corona by considering both vertices and edges simultaneously in forming the corona aproduct with other graphs, called vertex-edge corona. Further, we study the spectral polynomial for the vertex-edge corona of three arbitrary graphs, followed by some corollaries related to regular graphs for their spectrum, energy and equienergetic graphs.
Reference20 articles.
1. C. Adiga AND B. R. RaKshith, Spectra of graph operations based on corona and neighborhood corona of graphs $G$ and $K_1$, J. Int. Math. Virtual Inst., 5 (2015), 55-69.
2. C. Adiga, B. R. Rakshith and K. N. Subba Krishna, Spectra of extended neighborhood corona and extended corona of two graphs, Electron. J. Graph Theory Appl., 4 (2016), 101-110.
3. R. B. BAPAT, Graphs and Matrices, Springer, 2010.
4. S. Barik, S. Pati and B. K. Sharma, The spectrum of the corona of two graphs, SIAM J. Discrete Math., 21 (2007), 47-56.
5. H. CHEN AND L. LiAo, The normalized laplacian spectra of the corona and edge corona of two graphs, Linear Multilinear Algebra, 65 (2017), 582-592.