Results 11 to 20 of about 963 (204)
On the nullity of unicyclic graphs
Linear Algebra and its Applications, 2005 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we obtain the nullity set of n-vertex unicyclic graphs, and characterize the unicyclic graphs with extremal ...
Liu, Bolian, Xuezhong, Tan
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On the multiplicity of Laplacian eigenvalues for unicyclic graphs [PDF]
Czechoslovak Mathematical Journal, 2022 summary:Let $G$ be a connected graph of order $n$ and $U$ a unicyclic graph with the same order. We firstly give a sharp bound for $m_{G}(\mu )$, the multiplicity of a Laplacian eigenvalue $\mu $ of $G$. As a straightforward result, $m_{U}(1)\le n-2$. We
Wen, Fei, Huang, Qiongxiang
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The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter
Journal of MathematicsTopological invariants are key tools for studying the physicochemical and thermodynamic properties of chemical compounds. Recently, a new bond-additive distance-based graph invariant called the Mostar index has been developed.
Muhammad Amer Qureshi +4 more
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Restrained domination in unicyclic graphs
Discussiones Mathematicae Graph Theory, 2009 Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by $γ_r(G)$, is the minimum cardinality of a restrained ...
Hattingh, Johannes +4 more
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Computing the vertex separation of unicyclic graphs
Information and Computation, 2004 We describe an O(nlogn) algorithm for the computation of the vertex separation of unicyclic graphs. The algorithm also computes a linear layout with optimal vertex separation in the same time bound. Pathwidth, node search number and vertex separation are
Markov, Minko, Ellis, John
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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 International audienceLet 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
Ming Chau +3 more
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The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices
Journal of MathematicsTopological indices are widely used molecular structure descriptors in chemistry and pharmaceutics, which help analyze and predict the physicochemical properties and biological activity of compounds.
Zhenhua Su, Zikai Tang
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Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter
Journal of MathematicsFor a connected graph G and two real numbers a,b, the general degree–eccentricity index of G is given by DEIa,bG=∑v∈VGdGavecGbv, where VG represent the vertex set of graph G, dGv denotes the degree of vertex v, and ecGv is the eccentricity of v in G ...
Mesfin Masre
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Contraharmonic Index: Extremal Results for Unicyclic Graphs and Bounds for General Graphs
Journal of MathematicsLet G be a graph with edge set EG. The degree of a vertex w in G is denoted by dw. The contraharmonic index of G is defined as CHG=∑uv∈EGdu+dv−1du2+dv2.
Abdulaziz Mutlaq Alotaibi, Akbar Ali
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Unicyclic signed graphs with minimal energy
Discrete Applied Mathematics, 2017 A connected signed graph with n vertices is said to be unicyclic if its number of edges is n. The energy of a signed graph S of order n with eigenvalues x(1), x(2), ..., x(n) is defined as E(S)=Sigma(n)(j=1) |x(j)|. We obtain the integral representations
S. Pirzada +3 more
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