On families of graphs which are both adjacency equienergetic and distance equienergetic
Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 198-209pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: Let and be the adjacency and distance matrices of a graph G respectively. The adjacency energy or -energy of a graph G is defined as the sum of the absolute values of the eigenvalues of . Analogously, the -energy is defined to be the sum of the absolute values of the eigenvalues of . One of the interesting problems on graph energy is to characterize those graphs which are equienergetic with respect to both the adjacency and distance matrices. A weaker problem is to construct the families of graphs which are equienergetic with respect to both the adjacency and distance matrices. In this paper, we find the explicit relations between -energy and -energy of certain families of graphs. As a consequence, we provide an answer to the above open problem (Indulal in https://icgc2020.wordpress.com/invitedlectures, 2020; http://www.facweb.iitkgp.ac.in/rkannan/gma.html, 2020)| Item type | Current library | Status | Barcode | |
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School of Engineering & Technology Archieval Section | Not for loan | 2024-1559 |
Let and be the adjacency and distance matrices of a graph G respectively. The adjacency energy or -energy of a graph G is defined as the sum of the absolute values of the eigenvalues of . Analogously, the -energy is defined to be the sum of the absolute values of the eigenvalues of . One of the interesting problems on graph energy is to characterize those graphs which are equienergetic with respect to both the adjacency and distance matrices. A weaker problem is to construct the families of graphs which are equienergetic with respect to both the adjacency and distance matrices. In this paper, we find the explicit relations between -energy and -energy of certain families of graphs. As a consequence, we provide an answer to the above open problem (Indulal in https://icgc2020.wordpress.com/invitedlectures, 2020; http://www.facweb.iitkgp.ac.in/rkannan/gma.html, 2020)
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