Fractional Matching Preclusion for (Burnt) Pancake Graphs

Ma, Tianlong; Mao, Yaping; Cheng, Eddie; Melekian, Christopher

doi:10.1109/i-span.2018.00030

Cited by 4 publications

(5 citation statements)

References 22 publications

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“…Hung et al [18] considered Hamiltonian properties in faulty pancake graphs. By Lemmas 4.34, 4.35 and Theorem 3.5(i), we can determine the FMP number and FSMP number of P G n , which was also obtained in [24].…”

Section: Pancake Graphsmentioning

confidence: 59%

“…9, each red cycle represents P G i 3 for 1 ≤ i ≤ 4). By Lemmas 4.34, 4.35 and Theorem 3.5(i), we can determine the FMP number and FSMP number of P G n , which was also obtained in [24].…”

Section: Pancake Graphsmentioning

confidence: 59%

“…Lemma 4.40 [19] BP n is (n − 2)-fault Hamiltonian for n ≥ 3. By Lemmas 4.39, 4.40 and Theorem 3.5(i), we can determine the FMP number and FSMP number of BP n , which was also obtained in [24]. As applications, the FMP number and FSMP number of some well-known networks, such as the restricted HL-graph G n , the n-dimensional torus T k 1 ,••• ,kn , the recursive circulant graphs G(d n , d) and G(2 n , 4), the (n, k)-arrangement graph A n,k , the (n, k)-star graph S n,k , the pancake graph P G n and the burnt pancake graph BP n , are determined (see Table 1).…”

Section: Burnt Pancake Graphsmentioning

confidence: 60%

“…By Lemmas 4.39, 4.40 and Theorem 3.5(i), we can determine the FMP number and FSMP number of BP n , which was also obtained in [24].…”

Section: Burnt Pancake Graphsmentioning

confidence: 62%

“…In 2017, Liu and Liu [23] considered the FMP number and FSMP number of complete graphs, Petersen graph and twisted cubes. Later, Ma et al [24] obtained the FMP number and FSMP number of (burnt) pancake graphs. Ma et al [25] determined the FMP number and FSMP number of arrangement graphs.…”

Section: Introductionmentioning

confidence: 99%

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Fractional matching preclusion of graphs

Liu

2016

J Comb Optim

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Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. As a generalization of matching preclusion, the fractional matching preclusion number (FMP number for short) of a graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings, and the fractional strong matching preclusion number (FSMP number for short) of a graph is the minimum number of edges and/or vertices whose deletion leaves a resulting graph with no fractional perfect matchings. A graph G is said to be f -fault Hamiltonian if there exists a Hamiltonian cycle in G − F for any set F of vertices and/or edges with |F | ≤ f . In this paper, we establish the FMP number and FSMP number of (δ −2)-fault Hamiltonian graphs with minimum degree δ ≥ 3. As applications, the FMP number and FSMP number of some well-known networks are determined. they have no vertex in common. A k-cycle is a cycle with k vertices. A cycle is called a Hamiltonian cycle if it contains all vertices of the graph. A graph is said to be Hamiltonian

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Section: Pancake Graphsmentioning

confidence: 59%

Section: Pancake Graphsmentioning

confidence: 59%