Diameter variability of cycles and tori

Some diameter notions in lexicographic product of graphs

“…In [1], [2], the diameter variability of the product graphs are discussed. In [12], Wang et al studied the diameter variability of cycles and tori. Graham and Harary studied the diameter variability of hypercubes in [4].…”

Diameter Vulnerability of Directed Cycles and Directed Tori

“…Graham and Harary [3] were the first to study the problem of how the diameter can be affected when some edges are added or removed. The following parameters measuring the diameter vulnerability was defined in [4] for an undirected graph G: for an arbitrary positive integer k, define D −k (G) to be the minimum number of edges the addition of which reduces the diameter of G by at least k; D +k (G) to be the minimum number of edges the removal of which increases the diameter of G by at least k; D +0 (G) to be the maximum number of edges the removal of which does not change the diameter of G; D −0 (G) to be the maximum number of arcs the addition of which does not change the diameter of G. For convenience, D −1 (G) and D +1 (G) are written as D − (G) and D + (G), respectively.…”

Two-node-Hamiltonicity of enhanced pyramid networks

“…Topological properties of faulty networks have been investigated, such as computing diameter [2,33] fault diameter [2], wide diameter [2,26], routing [4], and embedding [3,[11][12][13][16][17][18][19][20][21]24,32,34]. This work concentrates on the fault-tolerant cycle embedding in an EPM.…”