Abstract
Let G be a connected graph with the vertex set V = {v(1), v(2),..., v(n)}, where n >= 2. Denote by d(i) the degree of the vertex vi for i = 1, 2,..., n. If v(i) and v(j) are adjacent in G, we write i similar to j, otherwise we write i not similar to j. The variable sum exdeg index and coindex of G are defined as SEIa(G) = Sigma (i similar to j)(a(di) + a(dj)) = Sigma(n)(i=1) diadi and (SEI) over bar (a)(G) = Sigma(i not similar to j)(a(di) + a(dj)) = (n)(i=1)(n - 1 - d(i))a(di), respectively, where 'a' is a positive real number different from 1. Some inequalities involving SEIa(G) or/and SEIa(G) are derived. Special cases of the obtained inequalities are also discussed for unicyclic graphs.