A Note on the Lower Bounds for the Energy of Graphs

Graph energy, denoted by ε(G), is defined as the sum of the absolute values of the eigenvalues of a graph. In this work, we present several lower bounds for ε(G) under structural constraints, including results for regular graphs that are triangle-free and quadrangle-free, bounds for quadrangle-free graphs under degree conditions, and bounds for graphs whose quadrangles are mutually disjoint. We also discuss lower bounds in terms of the vertex cover number β(G), with corollaries for bipartite graphs and results for specific families such as outerplanar and chordal graphs.

In 12th Graph Theory and Algebraic Combinatorics Conference (GTACC 12), Tafresh University