Broadcasting Algorithm on Large Chordal Ring of Degree Six Networks

The study of loop networks has been motivated mainly by conception problems in the construction of local area networks and in the design of topologies for parallel processing computer systems. This paper discusses the degree-diameter problem for chordal ring of degree six networks. We focus upon maximizing the number of vertices in the graph for given diameter and degree. We improve the result of Yebra et al. (1985) by finding that the family of triple loop graphs of the form G(4k
²
+ 2k + 1;2k + 1;2k
²
) has a larger number of nodes for diameter k than the family G(3k
²
+ 3k + 1;3k + 1;3k + 2) given by Yebra et al. (1985). Moreover, a broadcasting algorithm is defined for the largest chordal ring of degree six networks. It is shown that all nodes in the network can receive the message by time at most d+3 where d is the diameter of the graph