The spanning cyclability of Cayley graphs generated by transposition trees

Qiao, Hongwei; Sabir, Eminjan; Meng, Jixiang

doi:10.1016/j.dam.2022.12.005

Cited by 7 publications

(2 citation statements)

References 19 publications

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“…Yang and Hsu proved that the generalized Petersen graph GP(n, k) is spanning 2-cyclable for k ≤ 4 [24]. Recently, Qiao et al proved that the enhanced hypercube [25]. But up to date, no one has done anything about the spanning-edge-cyclability of specified networks.…”

Section: Conjecture 2 ([17]mentioning

confidence: 99%

Embedding Spanning Disjoint Cycles in Hypercube Networks with Prescribed Edges in Each Cycle

Wu,

Sabir

2023

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One of the important issues in evaluating an interconnection network is to study the hamiltonian cycle embedding problems. A graph G is spanning k-edge-cyclable if for any k independent edges e1,e2,…,ek of G, there exist k vertex-disjoint cycles C1,C2,…,Ck in G such that V(C1)∪V(C2)∪⋯∪V(Ck)=V(G) and ei∈E(Ci) for all 1≤i≤k. According to the definition, the problem of finding hamiltonian cycle focuses on k=1. The notion of spanning edge-cyclability can be applied to the problem of identifying faulty links and other related issues in interconnection networks. In this paper, we prove that the n-dimensional hypercube Qn is spanning k-edge-cyclable for 1≤k≤n−1 and n≥2. This is the best possible result, in the sense that the n-dimensional hypercube Qn is not spanning n-edge-cyclable.

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Section: Conjecture 2 ([17]mentioning

confidence: 99%

Embedding Spanning Disjoint Cycles in Hypercube Networks with Prescribed Edges in Each Cycle

Wu,

Sabir

2023

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“…pq where K p,q is the complete bipartite graph with bipartite sets containing p and q vertices, respectively. It is well known, as in e.g., [9,10]. Another result is due to Sedlacek [11], who derived a formula for the wheel on n + 1 vertices, W n+1 , which is formed from a cycle Cn on n vertices by adding a vertex adjacent to every vertex of C n .…”

Section: Introductionmentioning

confidence: 99%

Complexity of Some Types of Cyclic Snake Graphs

Mohamed,

Amin

2024

MMA

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The number of spanning trees in graphs (networks) is a crucial invariant, and it is also an important measure of the reliability of a network. Spanning trees are special subgraphs of a graph that have several important properties. First, T must span G, which means it must contain every vertex in graph G, if T is a spanning tree of graph G. T needs to be a subgraph of G, second. Stated differently, any edge present in T needs to be present in G as well. Third, G is the same as T if each edge in T is likewise present in G. In path-finding algorithms like Dijkstra's shortest path algorithm and A* search algorithm, spanning trees play an essential part. In those approaches, spanning trees are computed as component components. Protocols for network routing also take advantage of it. In numerous techniques and applications, minimum spanning trees are highly beneficial. Computer networks, electrical grids, and water networks all frequently use them. They are also utilized in significant algorithms like the min-cut max-flow algorithm and in graph issues like the travelling salesperson problem. In this paper, we use matrix analysis and linear algebra techniques to obtain simple formulas for the number of spanning trees of certain kinds of cyclic snake graphs.

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