Matching preclusion for k-ary n-cubes

Matching preclusion for vertex-transitive networks

“…(7) A balanced hypercube; (7) A recursive circulant G(2 m , 4); (8) k-ary n-cubes. Note that these results have been obtained in [1], [2], [3], [6], [8], [10], [12], [15] and [19], respectively and one can easily check that the results in these papers are consistent with those obtained by applying our results. Furthermore, we can apply our results to other particular vertex-transitive networks, such as folded k-cube graphs, Hamming graphs and halved cube graphs.…”

“…Until now, the matching preclusion numbers of lots of networks (graphs) have been computed, such as Petersen graph, hypercube, complete graphs and complete bipartite graphs [1], Cayley graphs generalized by transpositions and (n, k)-star graphs [2], augmented cubes [3], (n, k)-buddle-sort graphs [6], tori and related Cartesian products [8], burnt pancake graphs [10], balanced hypercubes [12], restricted HL-graphs and recursive circulant G(2 m , 4) [15], and k-ary n-cubes [19]. Their optimal solutions have been also classified.…”

Matching preclusion for n-grid graphs

“…The matching preclusion numbers and optimal matching preclusion sets of the following graphs were studied: Petersen graph, complete graph K n , complete bipartite graph K n,n and hypercube Q n by Brigham et al [3], complete bipartite graph K n,n+1 by Cheng et al [7], even order k-ary n-cube Q k n by Wang et al [21], tori and related Cartesian products by Cheng et al [11], balanced hypercube BH n by Lü et al [20], crossed cube CQ n by Cheng et al [17].…”

Super edge-connectivity and matching preclusion of data center networks

“…Until now, the matching preclusion number of numerous networks were calculated and the corresponding optimal solutions were obtained, such as the complete graph, the complete bipartite graph and the hypercube [6], Cayley graphs generated by 2-trees and hyper Petersen networks [10], Cayley graphs generalized by transpositions and (n, k)-star graphs [11], restricted HL-graphs and recursive circulant G(2 m , 4) [31], tori and related Cartesian products [12], (n, k)-bubble-sort graphs [13], balanced hypercubes [27], burnt pancake graphs [22], k-ary n-cubes [35], cube-connected cycles [25], vertex-transitive graphs [24], n-dimensional torus [23], binary de Bruijn graphs [26] and n-grid graphs [17]. For the conditional matching preclusion problem, it is solved for the complete graph, the complete bipartite graph and the hypercube [6], arrangement graphs [14], alternating group graphs and split-stars [15], Cayley graphs generated by 2-trees and the hyper Petersen networks [10], Cayley graphs generalized by transpositions and (n, k)-star graphs [11], burnt pancake graphs [8,22], balanced hypercubes [27], restricted HL-graphs and recursive circulant G(2 m , 4) [31], k-ary n-cubes [35], hypercube-like graphs [32] and cube-connected cycles [25]. Particularly, Lü et al [28] has proved recently that it is NP-complete to determine the matching preclusion number and conditional matching preclusion number of a connected bipartite graph.…”