### Journals Information

**
Mathematics and Statistics Vol. 12(4), pp. 331 - 338 DOI: 10.13189/ms.2024.120404 Reprint (PDF) (301Kb) **

## On Zagreb Energy of Certain Classes of Graphs

**S. Sripriya , A. Anuradha ^{*}**

Department of Mathematics, Faculty of Engineering & Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, Tamilnadu, India

**ABSTRACT**

Energy of the graph G is the sum of absolute values of eigenvalues of its adjacency matrix. Given a simple connected graph G, its first (second) Zagreb matrix is constructed by including the sum (product) of the degrees of each pair of adjacent vertices of G. Computation of sum of absolute eigen values of these matrices yields the corresponding Zagreb energies. In this paper, the first and second Zagreb energies of certain families of graphs have been computed and a criterion to discern the nature of graph G based on their energies is obtained. The paper focuses on the comparative analysis of first and second Zagreb energies in terms of regular graphs such as cycle graphs, bipartite and tripartite graphs. Our findings reveal that the second Zagreb energy is always greater than first Zagreb energy for all complete bipartite graphs of even order greater than or equal to 4. Also we have established that the same is the case for complete tripartite graphs too. Furthermore, we illustrate that the two Zagreb energies coincide exclusively for the complete bipartite graph with equal partite sets if and only if the graph is of order 2. Additionally, we provide a criterion leading to an infinite set of non-isomorphic Zagreb equi-energetic graphs for all r>1 within partite graphs. The computations of two Zagreb energies for graph operations like t-splitting graph and t-shadow graph are also illustrated. The first and second Zagreb energies for some specific graphs along with bounds on Zagreb energies for wheel graphs are also discussed.

**KEYWORDS**

t-Splitting Graph, t-Shadow Graph, First Zagreb Energy, Second Zagreb Energy

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] S. Sripriya , A. Anuradha , "On Zagreb Energy of Certain Classes of Graphs," Mathematics and Statistics, Vol. 12, No. 4, pp. 331 - 338, 2024. DOI: 10.13189/ms.2024.120404.

(b). APA Format:

S. Sripriya , A. Anuradha (2024). On Zagreb Energy of Certain Classes of Graphs. Mathematics and Statistics, 12(4), 331 - 338. DOI: 10.13189/ms.2024.120404.