$A_\alpha$-SPECTRA OF DUPLICATION CORONAS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 73
DOI: https://doi.org/10.56827/SEAJMMS.2024.2002.2
Author :
Nijara Konch (Department of Mathematics, D. C. B Girls College, K. K. Baruah Road, Jorhat, Assam, INDIA)
A. Bharali (Department of Mathematics, Dibrugarh University, Dibrugarh - 786004, Assam, INDIA)
H. S. Ramane (Department of Mathematics, Karnatak University, Dharwad, Karnataka, INDIA)
Sumanta Borah (Department of Mathematics, Dibrugarh University, Dibrugarh - 786004, Assam, INDIA)
Abstract
The convex combination of diagonal matrix $D(G)$ and adjacency matrix $A(G)$ defined as $A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G) \textrm{for} \alpha \in [0,1] $ is indeed a good choice to merge $A$-spectra and $Q$-spectra theories of graphs. In this work, we discuss $A_\alpha$-eigenvalues of duplication corona, duplication edge corona, duplication neighbourhood corona and vertex complemented corona. Motivated by these operations, we have defined duplication vertex complemented corona operation and obtained corresponding $A_\alpha$-eigenvalues. We have also suggested some infinite family of graphs based on these findings.
Keywords and Phrases
$A_\alpha$-spectra, duplication edge corona, duplication neighbourhood corona, vertex complemented corona, duplication vertex complemented corona.
A.M.S. subject classification
05C31, 05C50.
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