Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes
Parallel Computing
Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements
Theoretical Computer Science
Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Sciences: an International Journal
Edge-bipancyclicity of conditional faulty hypercubes
Information Processing Letters
Edge-pancyclicity and path-embeddability of bijective connection graphs
Information Sciences: an International Journal
Conditional fault Hamiltonicity of the complete graph
Information Processing Letters
Edge-bipancyclicity of a hypercube with faulty vertices and edges
Discrete Applied Mathematics
Information Processing Letters
The bipancycle-connectivity of the hypercube
Information Sciences: an International Journal
Edge-fault-tolerant bipanconnectivity of hypercubes
Information Sciences: an International Journal
Bipanconnectivity and Bipancyclicity in k-ary n-cubes
IEEE Transactions on Parallel and Distributed Systems
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Some results on topological properties of folded hypercubes
Information Processing Letters
Many-to-Many Disjoint Path Covers in the Presence of Faulty Elements
IEEE Transactions on Computers
Conditional fault hamiltonian connectivity of the complete graph
Information Processing Letters
Many-to-many disjoint paths in faulty hypercubes
Information Sciences: an International Journal
Long paths in hypercubes with a quadratic number of faults
Information Sciences: an International Journal
Long paths and cycles in hypercubes with faulty vertices
Information Sciences: an International Journal
Edge-fault-tolerant node-pancyclicity of twisted cubes
Information Processing Letters
Cycles passing through a prescribed path in a hypercube with faulty edges
Information Processing Letters
The spanning connectivity of folded hypercubes
Information Sciences: an International Journal
Edge-fault-tolerant diameter and bipanconnectivity of hypercubes
Information Processing Letters
Hi-index | 0.07 |
The complete graphs are an important class of graphs, and are also fundamental interconnection networks. Recently, Fu investigated their edge-fault-tolerant Hamiltonicity and Ho et al. investigated their edge-fault-tolerant Hamiltonian-connectivity. In this paper, we improve the result of Fu and point out that the proof of the result of Ho et al. fails. Then we consider the edge-fault-tolerant panconnectivity of the complete graphs and obtain the following result. Let F be any set of at most 2n-10 faulty edges in the complete graph K"n with n vertices, such that every vertex of the graph G=K"n-F is incident with at least three edges and G@?{K"8-E(K"4),K"1"0-E(K"5)}. Then G is nearly panconnected, i.e., for any two vertices u and v, there exists a path connecting u and v in G of any length from 3 to n-1. As a corollary, every edge in the graph G lies on a cycle of any length from 4 to n. Moreover, the number 2n-10 of faulty edges tolerated is sharp.