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Wide Diameters of Cartesian Product Graphs and Digraphs

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  • Jun-Ming Xu

    (Universtiy of Science and Technology of China)

Abstract

In graph theory and study of fault tolerance and transmission delay of networks, connectivity and diameter of a graph are two very important parameters and have been deeply studied by many authors. Wide diameter combining connectivity with diameter is a more important parameter to measure fault tolerance and efficiency of parallel processing computer networks and has received much attention in the recent years. Diameter with width k of a graph G is defined as the minimum integer d for which between any two distinct vertices in G there exist at least k internally disjoint paths of length at most d. In the present paper, the tight upper bounds of wide diameter of the Cartesian product graphs are obtained. Some known results can be deduced or improved from ours.

Suggested Citation

  • Jun-Ming Xu, 2004. "Wide Diameters of Cartesian Product Graphs and Digraphs," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 171-181, June.
    • Handle: RePEc:spr:jcomop:v:8:y:2004:i:2:d:10.1023_b:joco.0000031418.45051.8b
    DOI: 10.1023/B:JOCO.0000031418.45051.8b
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    Cited by:

    1. Sun-Yuan Hsieh & Pei-Yu Yu, 2007. "Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 153-162, February.

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