Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 2, pp. 7 – 13
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0084
More on second Zagreb energy of graphs
Mitesh J. Patel\(^{1,*}\), Kajal S. Baldaniya\(^{2}\) and Ashika Panicker\(^{1}\)
\(^{1}\) Department of Mathematics, Tolani College of Arts and Science, Adipur- Kachchh, Gujarat – INDIA.; miteshmaths1984@gmail.com (M.J.P) ; panickerashika@gmail.com (A.P)
\(^{2}\) Department of Mathematics, Gajwani Institute of Science and Technology, Adipur- Kachchh, Gujarat – INDIA.; kajalbaldaniya20@gmail.com (K.S.B)
Copyright © 2023 Mitesh J. Patel, Kajal S. Baldaniya and Ashika Panicker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 14, 2023 – Accepted: August 05, 2023 – Published: October 23, 2023
Abstract
Let \(G\) be a graph with \(n\) vertices. The second Zagreb energy of graph \(G\) is defined as the sum of the absolute values of the eigenvalues of the second Zagreb matrix of graph \(G\). In this paper, we derive the relation between the second Zagreb matrix and the adjacency matrix of graph \(G\) and derive the new upper bound for the second Zagreb energy in the context of trace. We also derive the second Zagreb energy of \(m-\)splitting graph and \(m-\)shadow graph of a graph.
Keywords:
Second Zagreb energy; \(m-\)splitting graph; \(m-\)shadow graph; regular graph