Merging in bipartite distance-regular graphs

Abstract

Merging the first and third classes in a connected graph is the operation of adding edges between all vertices at distance 3 in the original graph while keeping the original edges.Merging the first m classes in a connected graph is joining all the pairs of vertices with distance at most m in the graph with edges. In this paper, wedetermine when merging the first and third classes in a bipartite distance-regular graph produces a distance-regular graph. We also determine when merging the first m classes in a bipartite distance-regular graph produces a distance-regular graph.

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