engleski

On Sum-Balaban Index

The sum-Balaban index of a connected graph G is defined as J(G) = (m/+1) (Du+Dv)-1/2exp. where Du is the sum of distances between vertex u and all other vertices,  is the cyclomatic number, E(G) is the edge set, and m = E(G). We establish various upper and lower bounds for the sum-Balaban index and determine the trees with the largest, second-largest and third-largest as well as smallest, second-smallest and third-smallest sum Balaban indices among the n-vertex tree for n  6.

sum-Balaban index; sum J index; cyclomatic number; tree; sum of distances

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