Fault-Hamiltonicity of Product Graph of Path and Cycle
نویسندگان
چکیده
We investigate hamiltonian properties of Pm × Cn, m ≥ 2 and even n ≥ 4, which is bipartite, in the presence of faulty vertices and/or edges. We show that Pm×Cn with n even is strongly hamiltonianlaceable if the number of faulty elements is one or less. When the number of faulty elements is two, it has a fault-free cycle of length at least mn−2 unless both faulty elements are contained in the same partite vertex set; otherwise, it has a fault-free cycle of length mn−4. A sufficient condition is derived for the graph with two faulty edges to have a hamiltonian cycle. By applying fault-hamiltonicity of Pm × Cn to a two-dimensional torus Cm × Cn, we obtain interesting hamiltonian properties of a faulty Cm × Cn.
منابع مشابه
Deciding Graph non-Hamiltonicity via a Closure Algorithm
We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices P, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. A graph instance (G) is initially coded as exclusion set ...
متن کاملFault Hamiltonicity of the Shuffle - Cubes ∗
Hypercubes are famous interconnection networks. The shuffle cubes are proposed as its variation with lower diameter. In this paper, we concentrate on the fault tolerant hamiltonicity and hamiltonian connectivity of the shuffle cube. We say that a graph G is f-hamiltonian if there is a hamiltonian cycle in G − F and is f-hamiltonian connected if there is a hamiltonian path between any two vertic...
متن کاملOn the Fault Tolerance and Hamiltonicity of the Optical Transpose Interconnection System of Non-Hamiltonian Base Graphs
Hamiltonicity is an important property in parallel and distributed computation. Existence of Hamiltonian cycle allows efficient emulation of distributed algorithms on a network wherever such algorithm exists for linear-array and ring, and can ensure deadlock freedom in some routing algorithms in hierarchical interconnection networks. Hamiltonicity can also be used for construction of independen...
متن کاملTotal vertex irregularity strength of corona product of some graphs
A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...
متن کاملPanpositionable hamiltonicity of the alternating group graphs
The alternating group graph AGn is an interconnection network topology based on the Cayley graph of the alternating group. There are some interesting results concerning the hamiltonicity and the fault tolerant hamiltonicity of the alternating group graphs. In this article, we propose a new concept called panpositionable hamiltonicity. A hamiltonian graph G is panpositionable if for any two diff...
متن کامل