Let G be a finite connected graph. The eccentric connectivity index ξ^c(G) of G is defined as ξ^c(G)=∑v∈V(G)ec(υ)deg(υ), where ec(v) and deg(υ) denote the eccentricity and degree of a vertex v in G, respectivel...Let G be a finite connected graph. The eccentric connectivity index ξ^c(G) of G is defined as ξ^c(G)=∑v∈V(G)ec(υ)deg(υ), where ec(v) and deg(υ) denote the eccentricity and degree of a vertex v in G, respectively. In this paper, we give an asymptotically sharp upper bound on the eccentric connectivity index in terms of order and vertex-connectivity and in terms of order and edge-connectivity. We also improve the bounds for triangle-free graphs.展开更多
文摘Let G be a finite connected graph. The eccentric connectivity index ξ^c(G) of G is defined as ξ^c(G)=∑v∈V(G)ec(υ)deg(υ), where ec(v) and deg(υ) denote the eccentricity and degree of a vertex v in G, respectively. In this paper, we give an asymptotically sharp upper bound on the eccentric connectivity index in terms of order and vertex-connectivity and in terms of order and edge-connectivity. We also improve the bounds for triangle-free graphs.
