Bounds for eccentricity-based parameters of graphs

The eccentricity of a vertex u in a graph G, denoted by epsilon G(u), is the maximum distance from u to other vertices in G. We study extremal problems for the average eccentricity and the first and second Zagreb eccentricity indices, denoted by sigma 0(G), sigma 1(G), and sigma 2(G), respectively. These are defined by sigma 0(G) = 1 u is an element of V(G) epsilon G(u), sigma 1(G) = & sum; and sigma 2(G) = & sum; |V (G)| u is an element of V(G) epsilon 2 G(u),uv is an element of E(G) epsilon G(u)epsilon G(v). We study lower and upper bounds on these parameters among n-vertex connected graphs with fixed diameter, chromatic number, clique number, or matching number. Most of the bounds are sharp, with the corresponding extremal graphs characterized. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.