Results 21 to 30 of about 1,156,434 (264)
Wiener index in graphs given girth, minimum, and maximum degrees
Theory and Applications of Graphs, 2023 Let $G$ be a connected graph of order $n$. The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$.
Fadekemi J. Osaye +3 more
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Journal of Combinatorial Theory, Series B, 2008 An axis-parallel $d$--dimensional box is a Cartesian product $R_1 \times R_2 \times ... \times R_d$ where $R_i$ (for $1 \le i \le d$) is a closed interval of the form $[a_i, b_i]$ on the real line. For a graph $G$, its \emph{boxicity} $\boxi(G)$ is the minimum dimension $d$, such that $G$ is representable as the intersection graph of (axis--parallel ...
Chandran, L Sunil +2 more
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Random Graphs with a Fixed Maximum Degree [PDF]
SIAM Journal on Discrete Mathematics, 2020 We study the component structure of the random graph $G=G_{n,m,d}$. Here $d=O(1)$ and $G$ is sampled uniformly from ${\mathcal G}_{n,m,d}$, the set of graphs with vertex set $[n]$, $m$ edges and maximum degree at most $d$. If $m= n/2$ then we establish a threshold value $ _\star$ such that if $ _\star$ then w.h.p. there is a unique giant component
Frieze, Alan M., Tkocz, Tomasz
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A Different Short Proof of Brooks’ Theorem
Discussiones Mathematicae Graph Theory, 2014 Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.
Rabern Landon
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Low-diameter topic-based pub/sub overlay network construction with minimum–maximum node degree [PDF]
PeerJ Computer Science, 2021 In the construction of effective and scalable overlay networks, publish/subscribe (pub/sub) network designers prefer to keep the diameter and maximum node degree of the network low.
Semih Yumusak +3 more
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Extremal Statistics on Non-Crossing Configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We obtain several properties of extremal statistics in non-crossing configurations with n vertices. We prove that the maximum degree and the largest component are of logarithmic order, and the diameter is of order $\sqrt{n}$.
Anna Mier, Marc Noy
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Bounding the maximum likelihood degree [PDF]
Mathematical Research Letters, 2015 v2: final version, to appear in Math.
Budur, Nero, Wang, Botong
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Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
Journal of Mathematics, 2021 Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor.
Wenjie Ning, Kun Wang, Hassan Raza
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Equitable Coloring and the Maximum Degree
European Journal of Combinatorics, 1994 The equitable \(h\)-coloring conjecture says that a connected graph \(G\) is equitable \(h(G)\)-colorable if it is different from \(K_ n\), \(C_{2n+1}\) and \(K_{2n+1,2n+1}\) for all \(n\geq 1\). This conjecture is proved for graphs \(G\) with \(h(G)\geq | G|/2\) or \(h(G)\leq 3\), where \(h(G)\) is the maximum vertex degree of \(G\).
Chen, Bor-Liang +2 more
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Reducing the maximum degree of a graph by deleting vertices: the extremal cases
Theory and Applications of Graphs, 2018 Let $\lambda(G)$ denote the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. In a recent paper, we proved that if $n$ is the number of vertices of $G$, $k$ is the maximum
Peter Borg, Kurt Fenech
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