Results 11 to 20 of about 39,392 (275)
Extremal infinite graph theory
Discrete Mathematics, 2011 We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.
Maya Stein
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Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions
Discrete Mathematics, 1974 AbstractThe main result of this paper is that for a special, but rather wide class of “sample graphs”, the extremal graphs, i.e. the graphs of n vertices without subgraphs isomorphic to the sample graph and having maximum number of edges under this condition, have very simple and symmetric structure.
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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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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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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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Note on the temperature Sombor index
Vojnotehnički Glasnik, 2023 Introduction/purpose: The temperature of a vertex of a graph of the order n is defined as d/(n-d), where d is the vertex degree. The temperature variant of the Sombor index is investigated and several of its properties established. Methods: Combinatorial
Ivan Gutman
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Short proofs of some extremal results [PDF]
, 2013 We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have ...
Beck +11 more
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On the spread of outerplanar graphs
Special Matrices, 2022 The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n ...
Gotshall Daniel +2 more
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