The edge eccentric connectivity index of armchair polyhex nanotubes
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2015
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Abstract
Let f = uv be an edge in E(G). Then the degree of the edge f is defined to be deg(u)+deg(v)-2. For two edges f1 = u1v1, f2 = u2v2 in E(G), the distance between f1 and f2, denoted by ed (f1, f2), is defined to be ed (f1, f2) = min{d(u1, v1),d(u1, v2), d(u2, v1), d(u2, v2). The edge eccentricity of an edge f, denoted by ec (f), is defined as ec(f) = max{d(f, e) | e ϵ E(G)}. The edge eccentric connectivity index of G, denoted by ζc e(G) is defined as ζce(G) = Σ fϵE(G) deg(f)ec(f). In this paper exact formulas for the edge eccentric connectivity index of an armchair polyhex nanotube is given. © 2015 American Scientific Publishers.