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On the wiener index of unicyclic graphs

WebLiu described the relations between Wiener polarity index, Zagreb index, Wiener index, and hyper-Wiener index in [ ]; they also determined there the rst two smallest Wiener polarity indices among all unicyclic graphs. Recently, Du et al. obtained the smallest and largest Wiener polarity indices togetherwith thecorrespondinggraphs amongalltreeswith 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

Remarks on the Wiener index of unicyclic graphs SpringerLink

Web6 de abr. de 2024 · In the case of unicyclic graphs f(x) ... Mn – index, Hosoya … 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 … birdcage burton latimer https://petersundpartner.com

ON THE WIENER INDEX OF UNICYCLIC GRAPHS - DergiPark

WebThe maximum Wiener polarity index of unicyclic graphs [J]. Appl Math Comput, 2012, … Web16 de jan. de 2024 · The Wiener, Wiener polarity and the terminal Wiener indices are the distance based topological indices. In this paper, we described a linear time algorithm {\bf(LTA)} that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. 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 … dalry auctions scotland

On Minimum Wiener Polarity Index of Unicyclic Graphs with …

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On the wiener index of unicyclic graphs

Remarks on the Wiener index of unicyclic graphs SpringerLink

Web30 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 … Web15 de jun. de 2012 · The Wiener polarity index W p (G) of a graph G is the number of …

On the wiener index of unicyclic graphs

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WebThe Wiener index of a graph G is defined as W (G) = ∑ u,v dG(u, v), where dG(u, v) is … WebThe Wiener Index of Unicyclic Graphs with Girth and the Matching Number

WebIn this paper, we characterize n-vertex unicyclic graphs with girth k, having minimal Gutman index. Supported by the Natural Science Foundation of China (Nos. 11101245, 61103119, 10871205), the Natural Science Foundation of Shandong (No. ZR2011AQ005, No. BS2010SF017) and BMNSF (4112052). WebAbstract. The Wiener polarity index of a graph is the number of unordered pairs of vertices of such that the distance between and 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 …

WebHá 2 dias · In this paper, we obtain the graph with the least Wiener index among all the unicyclic graphs with n vertices and diameter d. Moreover, if 4≤d≤n-3, d≡0(mod 2), then the unicyclic graphs with ... WebHá 1 dia · The revised edge Szeged index of is defined as , where (resp., ) is the number …

Web9 de mar. de 2024 · Molecular trees and unicyclic graphs are characterized by …

WebDOI: 10.46793/match.88-1.179m Corpus ID: 245986474; Upper and Lower Bounds for … dalry auctions north ayrshireWeb1 de dez. de 2013 · In this paper, we obtain the graph with the least Wiener index … bird cage clock made in usaWebDOI: 10.46793/match.88-1.179m Corpus ID: 245986474; Upper and Lower Bounds for Generalized Wiener Indices on Unicyclic Graphs @article{MartinezPerez2024UpperAL, title={Upper and Lower Bounds for Generalized Wiener Indices on Unicyclic Graphs}, author={'Alvaro Mart'inez-P'erez and os'e M. Rodr'iguez}, journal={Match … dalry ayrshire deathsWebof the two vertices vi and vj in the graph G (i.e., the number of edges in a shortest path connecting vi and vj). Mathematical properties and applications of H are reported in [4, 9, 10, 21, 30]. Another distance-based topological indices of a graph G is the Wiener index W(G). As an oldest topological index, the Wiener index of a graph G ... birdcage comics cafeWebWiener index on unicyclic graphs, e.g. [4,8,11]. Section 4 of the aforementioned paper of Furtula et al. [15] is devoted to unicyclic graphs. Furthermore, we say that a graph on p + q vertices has a (p;q)-partition if it is bipartite and the … dalry auto shopWeb9 de mar. de 2024 · Molecular trees and unicyclic graphs are characterized by identifying extremal NI index. ... [37] Poulik S., Ghorai G., Determination of journeys order based on graph’s wiener absolute index with bipolar fuzzy information, Inf. Sci. 545 (2024) ... birdcage coil hfssWebThe 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]. dalry ayrshire history