A study of odd graphs as fault-tolerant interconnection networks

Optimal Independent Spanning Trees on Odd Graphs

“…Thus H 3 ∪ s 1 = 1, 2 , so by the previous case again x = 2, x = 1, and P is represented by [8,2,6,1,7,8,2].…”

“…It was proven in [6] that dist(u, v) = min{H uv , H uv }. Let r be the bitstring obtained by applying the bitwise Exclusive-OR (denoted by ⊕) operation to u and v, so r = r 1 r 2 .…”

Semi-distributed load balancing for massively parallel multicomputer systems

“…They have degree n, diameter k = n -1 and (~ = f ) nodes. The Odd graph 03 is the celebrated Peterson graph [21]. For every node x in On [21],…”

Embedding Algorithms for Bubble-Sort, Macro-star, and Transposition Graphs

“…If we classify the interconnection networks proposed up to now, we can divide them into the mesh variation with n×k nodes [9], the hypercube variation with 2 n nodes [2], [3], [10], the star graph variation with n! nodes [8], and the odd graph variation with combination 2n C n nodes [4]. A variation of the star graph represents nodes using n distinct symbols, and the number of nodes is approximately n!…”

“…The embedding of interconnection networks is intended to analyze the interrelationship between graphs to observe whether a certain graph G is included in or interrelated with another graph H. The evaluation of embedding is significant: if graph G can be efficiently embedded in graph H with less cost, then the method developed in the interconnection network with graph G can be used in the interconnection network with graph H at less cost [3], [4]. In previous works [5], [6], we analyzed embedding methods for some star variations such as star, matrix-star, Rotator-Faber-Moore, and pancake graphs.…”