Terminal Wiener Index for Graph Structures

The topological distance between a pair of vertices i and j, which is denoted by d(vi, vj), is the number of edges of the shortest path joining i and j. The Wiener index W(G) is the sum of distances between all pairs of vertices of a graph G. W(G) = i d(vi, vj |G) where d(vi, vj |G) is the distance between the vertices vi and vj in a graph. The Terminal Wiener index TW(G) is defined as the sum of the distance between all pairs of pendent vertices in a graph G. In this paper we analyze various types of trees, caterpillar graphs isomorphic to molecular structures and Terminal Wiener index for generalized graphs.

• J. Baskar Babujee
• J. Senbagamalar

• Graph
• Degree
• Distance
• Pendent vertex
• Wiener index
• Tree.

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