Results 1 to 10 of about 35,638 (292)
Graph Partitions in Chemistry [PDF]
Entropy, 2023 We study partitions (equitable, externally equitable, or other) of graphs that describe physico-chemical systems at the atomic or molecular level; provide examples that show how these partitions are intimately related with symmetries of the systems; and discuss how such a link can further lead to insightful relations with the systems’ physical and ...
Ioannis Michos, Vasilios Raptis
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Clique-partitioned graphs [PDF]
Discrete Applied Mathematics, 2022 A graph $G$ of order $nv$ where $n\geq 2$ and $v\geq 2$ is said to be weakly $(n,v)$-clique-partitioned if its vertex set can be decomposed in a unique way into $n$ vertex-disjoint $v$-cliques. It is strongly $(n,v)$-clique-partitioned if in addition, the only $v$-cliques of $G$ are the $n$ cliques in the decomposition.
Grahame Erskine +2 more
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Partitioning the vertex set of $G$ to make $G\,\Box\, H$ an efficient open domination graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs $G$ for which the Cartesian product $G \Box H$ is an efficient open domination graph when ...
Tadeja Kraner Šumenjak +3 more
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RNA graph partitioning for the discovery of RNA modularity: a novel application of graph partition algorithm to biology. [PDF]
PLoS One, 2014 Kim N, Zheng Z, Elmetwaly S, Schlick T.
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Opuscula Mathematica, 2023 A coalition in a graph \(G = (V, E)\) consists of two disjoint sets \(V_1\) and \(V_2\) of vertices, such that neither \(V_1\) nor \(V_2\) is a dominating set, but the union \(V_1 \cup V_2\) is a dominating set of \(G\). A coalition partition in a graph \
Teresa W. Haynes +4 more
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Mathematical Modelling and Control, 2021 In this paper, we study the problem of partitioning the vertex set of a planar graph with girth restriction into parts, also referred to as color classes, such that each part induces a graph with components of bounded order.
Chunyu Tian, Lei Sun
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On the Bounded Partition Dimension of Some Generalised Graph Structures
Journal of Mathematics, 2022 Consider λ to be a connected graph with a vertex set Vλ that may be partitioned into any partition set S. If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ..
Wajdi Alghamdi, Muhammad Ahsan Asim
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Fault-Tolerant Partition Resolvability of Cyclic Networks
Journal of Mathematics, 2021 Graph invariants provide an amazing tool to analyze the abstract structures of networks. The interaction and interconnection between devices, sensors, and service providers have opened the door for an eruption of mobile over the web applications ...
Kamran Azhar +3 more
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Graph partitioning: an updated survey
AKCE International Journal of Graphs and Combinatorics, 2023 Graph partitioning problem, which is one of the most important topics in graph theory, usually asks for a partition of the vertex set of a graph into pairwise disjoint subsets with various requirements. It comes from the well-known Max-Cut Problem: Given
Shufei Wu, Jianfeng Hou
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Dynamic Balanced Graph Partitioning [PDF]
SIAM Journal on Discrete Mathematics, 2020 This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes into $\ell$ clusters, each of size $k ...
Avin, Chen +4 more
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