On the wiener index of unicyclic graphs
WebA graph is unicyclic (or monocyclic) if it is connected and contains exactly one cycle. There is a rich literature on extremal problems regarding Wiener index on unicyclic graphs (for example, see [5, 13, 19, 22]). Section 4 of [21] is devoted to unicyclic graphs. Lin [17] studied the extreme Wiener index of trees with given number of even degree Web28 de mai. de 2009 · Then the Wiener index of G with respect to c is W ( G, c) = ∑ { x, y } ⊆ V c ( x) c ( y) d ( x, y). We note that for c ≡ 1 this yields the usual Wiener index, while for c ( x) = deg ( x) we obtain the Gutman index. The edge-Wiener index of a graph is connected to its Gutman index by the following inequality. Theorem 5.
On the wiener index of unicyclic graphs
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Web1 de jun. de 2016 · The Wiener index is the sum of distances between all pairs of distinct … Webwhere M 1 (Γ) and F (Γ) present the first Zagreb and forgotten indices of the (molecular) …
Web15 de nov. de 2024 · The name Wiener index or wiener number for the quantity defined … WebThe Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener polarity index of unicyclic graphs with any given maximum degree and girth, and characterize extremal …
Web15 de jun. de 2012 · The Wiener polarity index of a graph G is the number of unordered … http://www.kurims.kyoto-u.ac.jp/EMIS/journals/BMMSS/pdf/acceptedpapers/2011-03-039_R1.pdf
WebSZEGED INDEX OF A CLASS OF UNICYCLIC GRAPHS 1141 Lemma 3 ([10,18]). Among the n-vertex trees with n 4, S0 n is the unique graph with the second smallest Wiener index, which is equal to n2 n 2, and P0 n is the unique graph with the second largest Wiener index, which is equal to 1 6.n 3 7nC18/. The following lemma may be easily …
Web1 de set. de 1994 · Maximum Reciprocal Degree Resistance Distance Index of Unicyclic Graphs. Discrete Dynamics in Nature and Society 2024, 2024 , 1-14. https: ... The symmetry-moderated Wiener index of truncation graph, Thorn graph and Caterpillars. Discrete Applied Mathematics 2024, 269 , 41-51. https: ... grefrath kircheWeb17 de out. de 2016 · The Wiener index is the sum of distances between all pairs of … grefrath hotel grefrather hofWeb30 de out. de 2024 · Moreover, SAGE simulations on graphs with up to ten vertices confirm that the pair of graphs shown in Fig. 2 is the smallest and unique pair of D-cospectral graphs having different diameter and Wiener index.. Download : Download high-res image (45KB) Download : Download full-size image Fig. 1. Two graphs on four vertices which … grefrath isekWebOur paper is organized as follows: In Section 2, we give necessary definitions and state … grefrath marions tierparadiesWebSearch ACM Digital Library. Search Search. Advanced Search grefrath matziWebThe Wiener index of a graph G is defined as W (G) = ∑ u,v dG(u, v), where dG(u, v) is … grefrath mönchengladbach busWebThe maximum Wiener polarity index of unicyclic graphs [J]. Appl Math Comput, 2012, 218(20): 10149-10157. [9] BANDY J B A, MURTY U S R. Graph theory [M]. London: Springer, 2008. [10] LIU Bolian, HOU Huoquan, HUANG Yufen. On the Wiener polarity index of trees with maximum degree or given number of leaves [J]. grefrath kita