2025/07/01 by Samanta, Aniruddha
#05C22(primary) #05C35(secondary) #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2507.00798
Let G be a simple graph with the vertex cover number τ. The energy E(G) of G is the sum of the absolute values of all the adjacency eigenvalues of G . In this article, we establish E(G)≥ 2τ for several classes of graphs. The result significantly improves the known result E(G)≥ 2τ-2c for many classes of graphs, where c is the number of odd cycles.