Results 21 to 30 of about 1,191,800 (264)
Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings
Song Wen-Yao +2 more
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Average eccentricity, minimum degree and maximum degree in graphs [PDF]
Journal of Combinatorial Optimization, 2020 Let $G$ be a connected finite graph with vertex set $V(G)$. The eccentricity $e(v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$. The average eccentricity of $G$ is defined as $\frac{1}{|V(G)|}\sum_{v \in V(G)}e(v)$. We show that the average eccentricity of a connected graph of order $n$, minimum degree $δ$ and maximum degree $
Peter Dankelmann, Fadekemi Janet Osaye
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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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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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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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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 \(G\).
Bor-Liang Chen, Ko-Wei Lih, Pou-Lin Wu
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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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Vertex arboricity and maximum degree
Discrete Mathematics, 1995 This paper mainly proves that if a connected graph \(G= (V,E)\) is neither a cycle nor a clique, then there is a coloring of \(V\) with at most \(\lceil {{\Delta (G)} \over 2} \rceil\) colors such that all color classes induce forests and one of them is a minimum induced forest in \(G\).
Paul A. Catlin, Hong-Jian Lai
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Intersection Dimension and Maximum Degree
Electronic Notes in Discrete Mathematics, 2009 Abstract We show that the intersection dimension of graphs with respect to several hereditary properties can be bounded as a function of the maximum degree. As an interesting special case, we show that the circular dimension of a graph with maximum degree Δ is at most O ( Δ log Δ log log Δ ) .
N. R. Aravind, C. R. Subramanian 0001
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On the Concentration of the Maximum Degree in the Duplication-Divergence Models
SIAM Journal on Discrete Mathematics, 2021 We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Solé, Pastor-Satorras et al. in which the graph grows according to a duplication-divergence mechanism, i.e.
Alan M. Frieze +2 more
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