On families of graphs which are both adjacency equienergetic and distance equienergetic
Ramane, H. S.
On families of graphs which are both adjacency equienergetic and distance equienergetic - Vol.55(1), Mar - New Delhi Springer 2024 - 198-209p.
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)
Humanities and Applied Sciences
On families of graphs which are both adjacency equienergetic and distance equienergetic - Vol.55(1), Mar - New Delhi Springer 2024 - 198-209p.
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)
Humanities and Applied Sciences