Eccentric and Total Eccentric Connectivity Indices of Caterpillars

Document Type : Research Paper


1 University of Tehran, Tehran, Iran

2 University of Tehran, Iran


Consider a simple connected graph 􀜩 with the vertex set 􀜸􁈺􀜩􁈻. The eccentric and total connectivity indices of 􀜩 are defined as 􀟦􀯖􁈺􀜩􁈻 􀵌 Σ􀯩􀗐􀜸􁈺􀜩􁈻 􀝁􀜿􀯀􁈺􀝒􁈻􀝀􀝁􀝃􀯀􁈺􀝒􁈻 and 􀜧􀜥􁈺􀜩􁈻 􀵌 Σ􀯩􀗐􀜸􁈺􀜩􁈻 􀝁􀜿􀯀􁈺􀝒􁈻, respectively. Here, 􀝀􀝁􀝃􀯀􁈺􀝒􁈻 denotes the degree of a vertex 􀝒 and 􀝁􀜿􀯀􁈺􀝒􁈻 is its eccentricity. In this paper, these two indices are calculated for a given arbitrary caterpillar.