Journal article

Forwarding and optical indices of 4-regular circulant networks

Heng-Soon Gan, Hamid Mokhtar, Sanming Zhou

JOURNAL OF DISCRETE ALGORITHMS | ELSEVIER SCIENCE BV | Published : 2015

Abstract

An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by π(G,R). The edge-forwarding index π(G) is the minimum of π(G,R) over all possible all-to-all routings R, and the arc-forwarding index π→(G) is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by w(G,R) the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colour..

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