Geodesic
Note on the Unicyclic Graphs with the First Three Largest Wiener Indices
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 533

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Let $G=(V,E)$ be a simple connected graph with vertex set $V$ and edge set $E$. Wiener index $W(G)$ of a graph $G$ is the sum of distances between all pairs of vertices in $G$, i.e., $W(G) = \sum_{\{u,v\}\subseteq G}d_G(u,v)$, where $d_G(u,v)$ is the distance between vertices $u$ and $v$. In this note we give more precisely the unicyclic graphs with the first tree largest Wiener indices, that is, we found another class of graphs with the second largest Wiener index.
Classification : 05C35 05C12
Keywords: Unicyclic graphs, Wiener index, distance, extremal graphs 
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     title = {Note on the {Unicyclic} {Graphs} with the {First} {Three} {Largest} {Wiener} {Indices}},
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E. Glogić; Lj. Pavlović. Note on the Unicyclic Graphs with the First Three Largest Wiener Indices. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 533 . http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a5/