20.500.12556/RUL-182186 Subtree number versus Wiener index The subtree number $N(G)$ of a graph $G$ is defined as the number of non-empty subtrees of $G$. The Wiener index $W(G)$ of a graph $G$ is defined as the sum of distances over all pairs of vertices in $G$. It has been noted that, for many families of trees and graphs, the graphs that achieve the largest number of subtrees are exactly those that attain the smallest Wiener index, and vice versa. Consequently, it is often said that the subtree number and the Wiener index have a ”negative” correlation. In this paper, we show that, except for extremal graphs, this ”negative” correlation does not generally hold. In particular, for every $n \ge 14$, we construct a pair of unicyclic graphs $G$ and $H$, each having n vertices and identical degree sequences, such that $W(G) < W(H)$ and $N(G) < N(H)$. Furthermore, our construction shows that both differences, $N(H) − N(G)$ and $W(H) -W(G)$, grow unbounded as $n$ increases. subtree number Wiener index teorija grafov drevesa Wienerjev indeks true false true Angleški jezik Slovenski jezik Članek v reviji 2026-04-29 12:05:53 2026-04-29 12:05:56 2026-04-30 04:31:13 0000-00-00 00:00:00 2026 0 0 Str. 972-974 iss. 3 Vol. 96 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 519.17 3009-4399 10.46793/match.96-3.25225 276693507 match96n3_961-974.pdf match96n3_961-974.pdf 1 85EC85B1C104EC1E8FB4D5C05A352A0B 3f271dd31b3eeb68bfe170bf23cda2a86292d673a4045dee074eefc3625b8c0a 04c40b35-43b3-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233178 https://match.pmf.kg.ac.rs/issues/m96n3/m96n3_25225.html 1 c0ca450c-43b2-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233176 Fakulteta za matematiko in fiziko 0 0 0