Results 41 to 50 of about 2,717 (193)
Introducing New Exponential Zagreb Indices for Graphs
Journal of Mathematics, 2021 New graph invariants, named exponential Zagreb indices, are introduced for more than one type of Zagreb index. After that, in terms of exponential Zagreb indices, lists on equality results over special graphs are presented as well as some new bounds on ...
Nihat Akgunes, Busra Aydin
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Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs
Mathematics, 2022 Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex ...
Enqiang Zhu +2 more
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Spanning trees and even integer eigenvalues of graphs [PDF]
, 2014 For a graph $G$, let $L(G)$ and $Q(G)$ be the Laplacian and signless Laplacian matrices of $G$, respectively, and $\tau(G)$ be the number of spanning trees of $G$.
Ghorbani, Ebrahim
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Extremal Unicyclic Graphs With Minimal Distance Spectral Radius
Discussiones Mathematicae Graph Theory, 2014 The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3).
Lu Hongyan, Luo Jing, Zhu Zhongxun
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Further Results on the Resistance-Harary Index of Unicyclic Graphs
Mathematics, 2019 The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G.
Jian Lu +4 more
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AKCE International Journal of Graphs and Combinatorics, 2023 For a connected simple graph G, the inverse degree index and forgotten index are defined as [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] denotes the degree of vertex u in G.
Mohammad Ali Manian +2 more
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Some Results on the Independence Polynomial of Unicyclic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
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On Unicyclic Graphs Spectra: New Results
2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES), 2016 Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular class of unicyclic graphs G(q, n1) where q is the size of the unique cycle. Each vertex of the unique cycle is attached to n1 vertices. We provide the " exact values " of the extremal eigenvalues of the adjacency matrix A and the Laplacian ...
Hadji, Makhlouf, Chau, Ming
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Sharp Lower Bounds of the Sum-Connectivity Index of Unicyclic Graphs
Journal of Mathematics, 2021 The sum-connectivity index of a graph G is defined as the sum of weights 1/du+dv over all edges uv of G, where du and dv are the degrees of the vertices u and v in graph G, respectively.
Maryam Atapour
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On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
Journal of Applied Mathematics, 2014 The 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 ...
Jianping Ou, Xing Feng, Saihua Liu
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