Results 1 
4 of
4
Fault diameter of Cartesian product graphs
 INFORMATION PROCESSING LETTERS 93 (2005) 245–248
, 2005
"... The (k − 1)fault diameter Dk(G) of a kconnected graph G is the maximum diameter of G − F for any F ⊂ V(G) with F  <k. Krishnamoorthy and Krishnamurthy first proposed this concept and gave Dκ(G1)+κ(G2)(G1 × G2) � Dκ(G1)(G1) + Dκ(G2)(G2) when κ(G1 × G2) = κ(G1) + κ(G2), whereκ(G) is the conne ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
The (k − 1)fault diameter Dk(G) of a kconnected graph G is the maximum diameter of G − F for any F ⊂ V(G) with F  <k. Krishnamoorthy and Krishnamurthy first proposed this concept and gave Dκ(G1)+κ(G2)(G1 × G2) � Dκ(G1)(G1) + Dκ(G2)(G2) when κ(G1 × G2) = κ(G1) + κ(G2), whereκ(G) is the connectivity of G. This paper gives a counterexample to this bound and establishes Dk1+k2 (G1 × G2) � Dk1 (G1) + Dk2 (G2) + 1foranykiconnected graph Gi and ki � 1for i = 1, 2.
Wide Diameters of Cartesian product graphs and digraphs
 J Comb Optim
, 2004
"... 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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
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.
ON GENERALIZED WIDE DIAMETER OF GRAPHS
"... Abstract. The wide diameter of a graph is a natural generalization of diameter in a graph when we take account of the connectivity of the graph. In this paper, we define the generalized wide diameter of a graph and show that every kregular kconnected graph on n vertices has generalized kdiameter a ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The wide diameter of a graph is a natural generalization of diameter in a graph when we take account of the connectivity of the graph. In this paper, we define the generalized wide diameter of a graph and show that every kregular kconnected graph on n vertices has generalized kdiameter at most n=2 and this upper bound cannot be improved when n = 4k ¡ 6+ i(2k ¡ 4). 1.
ON CONTAINER LENGTH AND WIDEDIAMETER IN UNIDIRECTIONAL HYPERCUBES
"... Abstract. In this paper, two unidirectional binary ncubes, namely, Q1(n) andQ2(n), proposed as highspeed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum faulttolerant container froma tob is at mostn+2 whetheraandb are inQ1(n) or inQ2(n). Fu ..."
Abstract
 Add to MetaCart
Abstract. In this paper, two unidirectional binary ncubes, namely, Q1(n) andQ2(n), proposed as highspeed networking schemes by Chou and Du, are studied. We show that the smallest possible length for any maximum faulttolerant container froma tob is at mostn+2 whetheraandb are inQ1(n) or inQ2(n). Furthermore,we prove that the widediameters ofQ1(n) andQ2(n) are equal ton + 2. At last, we show that a conjecture proposed by Jwo and Tuan is true. 1.