University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2 Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday) 2011 04 01 Eccentric and Total Eccentric Connectivity Indices of Caterpillars 39 44 5164 10.22052/ijmc.2011.5164 EN KH. FATHALIKHANI University of Tehran, Tehran, Iran H. YOUSEFI-AZARI University of Tehran, Iran Journal Article 2014 04 22 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. eccentric connectivity index Total eccentricity index Caterpillar https://ijmc.kashanu.ac.ir/article_5164_5eab17f138e0f73210f23c5b0adcbc49.pdf