***** To join INSNA, visit http://www.insna.org ***** Hi,
I wanted to ask a quick question on graph theory.. I'd be very thankful if you could help me with it..
A k-regular simple graph G on v nodes is strongly k-regular
if there exist positive integers (k,s,m) such that every vertex has k neighbors (i.e., the graph is regular), every adjacent pair of vertices has 's' common neighbors, and every nonadjacent
pair has 'm' common neighbors (West 2000, pp. 464-465).
I am looking for graphs for which the last property (that every nonadjacent pair has m common neighbors) is relaxed. So, the nonadjacent pairs might have different number of common neighbours, while adjacent pairs have same number of common neighbors. (a cycle
graph with n>5 is an example of such a graph). Do you know whether this family of graphs have a particular name in the literature so that I can check for their properties?
Thank you very much in advance!
European University Institute
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