Abstract
The Wiener polarity index WP of a graph G is the number of unordered pairs of vertices u,v of G such that the distance dG(u, v) between u and v is 3. Cycle-block graph is a connected graph in which every block is a cycle. In this paper, we determine the maximum and minimum Wiener polarity index of cycle-block graphs and describe their extremal graphs; the extremal graphs of 4-uniform cactus with respect to Wiener polarity index are also discussed.
Highlights
Let G = (V, E) be a connected simple graph
The distance dG(u, V) between the vertices u and V of G is defined as the length of a shortest path connecting u and V
NGi (u) = {V ∈ V(G) | dG(u, V) = i} is called the ith neighbor set of u. d(u) = |NG1 (u)| is called the degree of u
Summary
We discuss the extremal graphs of Wiener polarity index of cycle-block graphs with g ≥ 5 and 4-uniform cactus. 2. The Extremal Graphs of Wiener Polarity Index of Cycle-Block Graphs with g ≥ 5 We characterize the maximum and minimum Wiener polarity index of the cycle-block graphs with g ≥ 5.
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