The Edge Version of Eccentric Connectivity Index
نویسندگان
چکیده
Let G be a connected graph with vertex set V (G) and edge set E(G). The eccentric connectivity index of G, denoted by ξc(G), is defined as ∑ v∈V (G) deg(v)ec(v), where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. In this paper, we propose the edge version of the above index, the edge eccentric connectivity index of G, denoted by ξc e(G), which is defined as ξc e(G) = ∑ f∈E(G) deg(f)ec(f), where deg(f) is the degree of an edge f and ec(f) is its eccentricity. Various upper and lower bounds are obtained for this index of connected graphs in terms of order, size, girth and the first Zagreb index of G, respectively.
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