The Eccentric Connectivity Index of Some Special Graphs

Document Type: Research Paper


Yazd University, Iran


If 􀜩 is a connected graph with vertex set 􀜸, then the eccentric connectivity index of 􀜩, 􀣈􀡯􁈺􀜩􁈻, is defined as Σ􀯩􀗐􀯏 deg􁈺􀝒􁈻 􀝁􀜿􀜿􁈺􀝒􁈻 where deg 􁈺􀝒􁈻 is the degree of a vertex 􀝒 and 􀝁􀜿􀜿􁈺􀝒􁈻 is its eccentricity. Let A, B and C are families of graphs made by joining 􀜲􀯡 to 􀜭􀯠, made by putting 􀜭􀯠instead of each vertex in 􀜲􀯡 and made by putting 􀜥􀯠 instead of each vertex in 􀜲􀯡, respectively. In this paper we compute the eccentric connectivity index of these families of graphs.