Results 1 to 10 of about 590 (74)
Reinforcement Number of a Graph with respect to Half-Domination
In this paper, we introduce the concept of reinforcement number with respect to half-domination and initiate a study on this parameter. Furthermore, we obtain various upper bounds for this parameter. AMS subject classification: 05C38, 05C40, 05C69.
G. Muhiuddin+4 more
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Computational complexity of network vulnerability analysis
Residual closeness is recently proposed as a vulnerability measure to characterize the stability of complex networks. Residual closeness is essential in the analysis of complex networks, but costly to compute.
Berberler Murat Erşen
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On Proper (Strong) Rainbow Connection of Graphs
A path in an edge-colored graph G is called a rainbow path if no two edges on the path have the same color. The graph G is called rainbow connected if between every pair of distinct vertices of G, there is a rainbow path.
Jiang Hui+3 more
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Some results on the total proper k-connection number
In this paper, we first investigate the total proper connection number of a graph GG according to some constraints of G¯\overline{G}. Next, we investigate the total proper connection numbers of graph GG with large clique number ω(G)=n−s\omega \left(G)=n ...
Ma Yingbin, Zhang Hui
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A set S ⊆ V (G) is a vertex k-cut in a graph G = (V (G), E(G)) if G − S has at least k connected components. The k-connectivity of G, denoted as κk(G), is the minimum cardinality of a vertex k-cut in G. We give several constructions of a set S such that (
Erker Tjaša Paj, Špacapan Simon
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On the connectivity of the disjointness graph of segments of point sets in general position in the plane [PDF]
Let $P$ be a set of $n\geq 3$ points in general position in the plane. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in $D(P)$ if and only ...
J. Leaños+2 more
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Conflict-Free Vertex Connection Number At Most 3 and Size of Graphs
A path in a vertex-coloured graph is called conflict-free if there is a colour used on exactly one of its vertices. A vertex-coloured graph is said to be conflict-free vertex-connected if any two distinct vertices of the graph are connected by a conflict-
Doan Trung Duy, Schiermeyer Ingo
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More on the Rainbow Disconnection in Graphs
Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-
Bai Xuqing+3 more
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Generalized 4-connectivity of hierarchical star networks
The connectivity is an important measurement for the fault-tolerance of a network. The generalized connectivity is a natural generalization of the classical connectivity. An SS-tree of a connected graph GG is a tree T=(V′,E′)T=\left(V^{\prime} ,E^{\prime}
Wang Junzhen, Zou Jinyu, Zhang Shumin
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Large Contractible Subgraphs of a 3-Connected Graph
Let m ≥ 5 be a positive integer and let G be a 3-connected graph on at least 2m + 1 vertices. We prove that G has a contractible set W such that m ≤ W ≤ 2m − 4.
Karpov Dmitri V.
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