Eccentric and Total Eccentric Connectivity Indices of Caterpillars

FATHALIKHANI, KH.; YOUSEFI-AZARI, H.

doi:10.22052/ijmc.2011.5164

Eccentric and Total Eccentric Connectivity Indices of Caterpillars

Document Type : Research Paper

Authors

KH. FATHALIKHANI ¹

H. YOUSEFI-AZARI ²

¹ University of Tehran, Tehran, Iran

² University of Tehran, Iran

10.22052/ijmc.2011.5164

Abstract

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.

Keywords

eccentric connectivity index

Total eccentricity index

Caterpillar