The

Based on (revised) Szeged index of a graph and the Steiner k-Wiener index of a tree, we introduce the k-Szeged index S z k...
Ausführliche Beschreibung

Based on (revised) Szeged index of a graph and the Steiner k-Wiener index of a tree, we introduce the k-Szeged index S z k ( G ) and revised k-Szeged index S z k ⁎ ( G ) of a graph G = ( V , E ) , defined as S z k ⁎ ( G ) = ∑ e = u v ∈ E ( G ) ∑ i = 1 k − 1 ( n u ( e ) + n 0 ( e ) 2 i ) ( n v ( e ) + n 0 ( e ) 2 k − i ) and S z k ( G ) = ∑ e = u v ∈ E ( G ) ∑ i = 1 k − 1 ( n u ( e ) i ) ( n v ( e ) k − i ) , where n u ( e ) , n v ( e ) and n 0 ( e ) denote respectively the number of vertices of G lying closer to vertex u than to vertex v, the number of vertices of G lying closer to vertex v than to vertex u and the number of vertices with equal distance to u and v. In this paper, we first determine upper and lower bounds of (revised) k-Szeged indices of a connected g... Ausführliche Beschreibung