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Wiener index of quadrangulation graphs
Discrete Applied Mathematics, 2021 The Wiener index of a graph $G$, denoted $W(G)$, is the sum of the distances between all pairs of vertices in $G$. É. Czabarka, et al. conjectured that for an $n$-vertex, $n\geq 4$, simple quadrangulation graph $G$, \begin{equation*}W(G)\leq \begin{cases} \frac{1}{12}n^3+\frac{7}{6}n-2, &\text{ $n\equiv 0~(mod \ 2)$,}\\ \frac{1}{12}n^3+\frac{11}{12}
Ervin Györi +2 more
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Hosoya Polynomials Of Some Semiconducotors
Journal of Kufa for Mathematics and Computer, 2014 The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x = 1 is equal to the Wiener index and second derivative at x =1 is equal to the hyperï€Wiener index.
Azeez Lafta Jabir +2 more
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The Wiener index of signed graphs [PDF]
Applied Mathematics and Computation, 2022 The Wiener index of a graph $W(G)$ is a well studied topological index for graphs. An outstanding problem of Šolt{é}s is to find graphs $G$ such that $W(G)=W(G-v)$ for all vertices $v\in V(G)$, with the only known example being $G=C_{11}$. We relax this problem by defining a notion of Wiener indices for signed graphs, which we denote by $W_σ(G)$, and ...
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Hosoya and Harary Polynomials of Hourglass and Rhombic Benzenoid Systems
Journal of Chemistry, 2020 In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound.
Zhong-Lin Cheng +4 more
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On the parity of the Wiener index
European Journal of Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephan G. Wagner, Hua Wang 0003
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A Note on “Wiener Index of a Fuzzy Graph and Application to Illegal Immigration Networks”
Applied Sciences, 2021 Connectivity parameters have an important role in the study of communication networks. Wiener index is such a parameter with several applications in networking, facility location, cryptology, chemistry, and molecular biology, etc.
Hoon Lee, Xue-gang Chen, Moo Young Sohn
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Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
Journal of Mathematics, 2021 Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively.
Shouliu Wei +3 more
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Tail Bounds for the Wiener Index of Random Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 Upper and lower bounds for the tail probabilities of the Wiener index of random binary search trees are given. For upper bounds the moment generating function of the vector of Wiener index and internal path length is estimated.
Tämur Ali Khan, Ralph Neininger
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Sharp bounds and normalization of Wiener-type indices. [PDF]
PLoS ONE, 2013 Complex networks abound in physical, biological and social sciences. Quantifying a network's topological structure facilitates network exploration and analysis, and network comparison, clustering and classification.
Dechao Tian, Kwok Pui Choi
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Wiener, edge-Wiener, and vertex-edge-Wiener index of Basilica graphs
Discrete Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matteo Cavaleri +3 more
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