NEW INEQUALITIES FOR EIGENVALUE-BASED GRAPH DESCRIPTORS

This paper establishes better lower bounds for the Estrada index of graphs through spectral graph theory. For an n-vertex graph G with m edges and t triangles, we prove that EE(G) ≥ √√n² + ۲mn + ۲nt, significantly improving previous results. Furthermore, we derive energy-dependent bounds that refine existing estimates for both general and bipartite graphs. The equality conditions are fully characterized, revealing extremal graph classes. Our results advance the theoretical understanding of spectral graph descriptors with applications in molecular chemistry and network science.

کلیدواژه ها:

spectrum of graph ، adjacency matrix ، bipartite graph