Super restricted edge connected Cartesian product graphs

Liu, Juan; Chen, Xing; Meng, Jixiang

doi:10.1016/j.ipl.2009.02.025

Cited by 6 publications

(2 citation statements)

References 14 publications

(18 reference statements)

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“…Shieh [4] characterized the super edge-connected Cartesian product graphs of two maximally edge-connected regular graphs. For the results on the restricted edge-connectivity of Cartesian product graphs, see [5][6][7] for references.…”

Section: Introductionmentioning

confidence: 99%

The Restricted Edge-Connectivity of Strong Product Graphs

Ye,

Tian

2024

Axioms

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The restricted edge-connectivity of a connected graph G, denoted by λ′(G), if it exists, is the minimum cardinality of a set of edges whose deletion makes G disconnected, and each component has at least two vertices. It was proved that λ′(G) exists if and only if G has at least four vertices and G is not a star. In this case, a graph G is called maximally restricted edge-connected if λ′(G)=ξ(G), and a graph G is called super restricted edge-connected if each minimum restricted edge-cut isolates an edge of G. The strong product of graphs G and H, denoted by G⊠H, is the graph with the vertex set V(G)×V(H) and the edge set {(x1,y1)(x2,y2)|x1=x2 and y1y2∈E(H); or y1=y2 and x1x2∈E(G); or x1x2∈E(G) and y1y2∈E(H)}. In this paper, we determine, for any nontrivial connected graph G, the restricted edge-connectivity of G⊠Pn, G⊠Cn and G⊠Kn, where Pn, Cn and Kn are the path, cycle and complete graph of order n, respectively. As corollaries, we give sufficient conditions for these strong product graphs G⊠Pn, G⊠Cn and G⊠Kn to be maximally restricted edge-connected and super restricted edge-connected.

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Section: Introductionmentioning

confidence: 99%

The Restricted Edge-Connectivity of Strong Product Graphs

Ye,

Tian

2024

Axioms

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“…Thus they are more refined measures of reliability for multiprocessor systems. The restricted connectivity, super connectivity and extra connectivity of many interconnection networks have been explored [2], [3], [4], [5], [10], [11], [29], [37], [44], [51], [15], [38], [39], [40], [31], [44], [28], [41], [42], [27], [33], [35], [19], [30], [32], [50], [51], [26], [48], [23], [44], [46], [24], [9], [49], [45], [47].…”

Section: Introductionmentioning

confidence: 99%

From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach

Zhu¹,

Ma²,

Guo³

et al. 2016

Preprint

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We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's connectivity is the minimum number of nodes, whose removal will cause the network disconnected. It is a basic and important measure for the network's reliability, hence its overall robustness. Several conditional connectivities have been proposed in the past for the purpose of accurately reflecting various realistic network situations, with extra connectivity being one such conditional connectivity. In this paper, we will use isoperimetric properties of the hypercube network to obtain its extra connectivity. The result of the paper for the first time establishes a relationship between the age-old isoperimetric problem and network connectivity.

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Super restricted edge-connectivity of graphs with diameter 2

Shang

Zhang

2013

Discrete Applied Mathematics

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Super restricted edge connected Cartesian product graphs

Cited by 6 publications

References 14 publications

The Restricted Edge-Connectivity of Strong Product Graphs

The Restricted Edge-Connectivity of Strong Product Graphs

From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach

Super restricted edge-connectivity of graphs with diameter 2

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