Wide Diameter Of The Graph Parameters

Graph parameters such as connectivity and diameter have been studiedextensively due to their intrinsic in graph theory, Conbinatorics and theirrelations to (and application in)fault tolerence and transmission delay incommunication networks. The advent of VLSI technology and fiber opticsmaterial science has enabled us to design massively parallel processingcomputer systems and fast and complicated communications networks. Allthese systems increase their reliability by studying (among other) theexistence of two (or more) disjoint paths connecting any two nodes. Tosatisfy all these demands, we generalize diameter of graphs.wide-diameter,fault-diameter and Rabin number is the generalize diameter.In this paper, we mainly study generalized wide-diameter of double loopnetworks and the relations of graph parameters.In the following, we list the main works of our paper.1. We study the wide-diameter and Rabin number of double loopnetwork C(n;1,a). d₂ (G(n;1, s)) ≤d_L +1, r₂(G(n;1,s)) ≤d_L +12. We find the number of double loop networks C(n;a,b) which are notisomorphous and the parameters which are related to wide-diameter.3. Because double loop network is symmetric and vertex-transitive.We find the value of the 4-wide diameter of C(n;1,a) if we can solve thewide-distance between node O and nodes 1,2,a.4. We also study the fault-diameter of C(2n;1,n).5. We discuss the function of h(n,k,d).