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- W3140880374 abstract "For a connected graph $G$, the Wiener index, denoted by $W(G)$, is the sum of the distance of all pairs of distinct vertices and the eccentricity, denoted by $varepsilon(G)$, is the sum of the eccentricity of individual vertices. In cite{Kc}, the authors posed a conjecture which states that given a graph $G$ with at least three vertices, the difference between $W(G)$ and $varepsilon(G)$ decreases when an edge is contracted and proved that the conjecture is true when $e$ is a bridge. In this manuscript, we confirm that the conjecture is true for any connected graph $G$ with at least three vertices irrespective of the nature of the edge chosen." @default.
- W3140880374 created "2021-04-13" @default.
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- W3140880374 date "2021-04-07" @default.
- W3140880374 modified "2023-09-25" @default.
- W3140880374 title "Proof of a Conjecture on Wiener Index and Eccentricity of a graph due to edge contraction" @default.
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