Results 11 to 20 of about 39,296 (257)
Construction Algorithm of Given Girth Graphs Based on Quantum Evolution [PDF]
Jisuanji gongcheng, 2017 To construct an extremal graph with a given girth is still a challenging problem of graph theory.Especially when the vertex number increasex combination explosion will appear.Thus,this paper proposes an algorithm for constructing graphs with given girth ...
FENG Xiaohua,SUN Yongqi
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Ars Mathematica Contemporanea, 2019 Summary: Let \(G\) be a ribbon graph and \(\mu (G)\) be the number of components of the virtual link formed from \(G\) as a cellularly embedded graph via the medial construction. In this paper we first prove that \(\mu (G) \leq f(G) + \gamma (G)\), where \(f(G)\) and \(\gamma (G)\) are the number of boundary components and Euler genus of \(G ...
Jin, Xian'an, Yan, Qi
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On the graph connectivity and the variable sum exdeg index
AIMS Mathematics, 2021 Topological indices are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. The variable sum exdeg index $SEI_{a}(G)$ of a graph $G$ is defined as $\sum _{u\in V(G)}d_{G}(u)a^{d_ ...
Jianwei Du, Xiaoling Sun
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Extreme Monophonic Graphs and Extreme Geodesic Graphs
Tamkang Journal of Mathematics, 2016 For a connected graph $G=(V,E)$ of order at least two, a chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A monophonic set of $G$ is a set $S$ of vertices such that every vertex of $G$ lies on a monophonic path joining some pair of vertices in $S$.
P. Titus, A.P Santhakumaran
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Extremal Graph Realizations and Graph Laplacian Eigenvalues
SIAM Journal on Discrete Mathematics, 2023 For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygon) associated with the first (non-trivial) eigenvalue. In this paper, we generalize this relationship.
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Solution to the minimum harmonic index of graphs with given minimum degree [PDF]
Transactions on Combinatorics, 2018 The harmonic index of a graph $G$ is defined as $ H(G)=\sum\limits_{uv\in E(G)}\frac{2}{d(u)+d(v)}$, where $d(u)$ denotes the degree of a vertex $u$ in $G$. Let $\mathcal{G}(n,k)$ be the set of simple $n$-vertex graphs with minimum degree at least $k$
Meili Liang, Bo Cheng, Jianxi Liu
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Graph Entropy Based on Strong Coloring of Uniform Hypergraphs
Axioms, 2021 The classical graph entropy based on the vertex coloring proposed by Mowshowitz depends on a graph. In fact, a hypergraph, as a generalization of a graph, can express complex and high-order relations such that it is often used to model complex systems ...
Lusheng Fang +3 more
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Strong Forms of Stability from Flag Algebra Calculations [PDF]
, 2018 Given a hereditary family $\mathcal{G}$ of admissible graphs and a function $\lambda(G)$ that linearly depends on the statistics of order-$\kappa$ subgraphs in a graph $G$, we consider the extremal problem of determining $\lambda(n,\mathcal{G})$, the ...
Pikhurko, Oleg +2 more
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Extremal properties of distance-based graph invariants for $k$-trees [PDF]
Mathematica Bohemica, 2018 Sharp bounds on some distance-based graph invariants of $n$-vertex $k$-trees are established in a unified approach, which may be viewed as the weighted Wiener index or weighted Harary index.
Minjie Zhang, Shuchao Li
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On the sum of powers of the $ A_{\alpha} $-eigenvalues of graphs
Mathematical Modelling and Control, 2022 Let $ A(G) $ and $ D(G) $ be the adjacency matrix and the degree diagonal matrix of a graph $ G $, respectively. For any real number $ \alpha \in[0, 1] $, Nikiforov recently defined the $ A_{\alpha} $-matrix of $ G $ as $ A_{\alpha}(G) = \alpha D(G)+(1 ...
Zhen Lin
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