engleski

On the general sum-connectivity index of trees

The general sum-connectivity index of a graph G is defined as chi(alpha)(G) = Sigma(uvE(G))(d(u) + d(v))(alpha) where du denotes the degree of vertex u in G, E(G) denotes the edge set of G and alpha is a real number. We determine the maximum value for the general sum-connectivity indices of n-vertex trees and the corresponding extremal trees for alpha < alpha(0), where alpha(0) = -4.3586... is the unique root of the equation 4(alpha) - 5(alpha)/5(alpha) - 6(alpha) = 3.

general sum-connectivity index; sum-connectivity index; first Zagreb index; degree; trees

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