Abstract.
Given a connected graph G, we say that a set C⊆V(G) is convex in G if, for every pair of vertices x,y∈C, the vertex set of every x-y geodesic in G is contained in C. The cardinality of a maximal proper convex set in G is the convexity number of G. In this paper, we characterize the convex sets of graphs resulting from some binary operations, and compute the convexity numbers of the resulting graphs.
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Received: October, 2001 Final version received: September 4, 2002
Acknowledgments. The authors would like to thank the referee for the helpful suggestions and useful comments.
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Canoy, Jr., S., Garces, I. Convex Sets Under Some Graph Operations. Graphs Comb 18, 787–793 (2002). https://doi.org/10.1007/s003730200065
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DOI: https://doi.org/10.1007/s003730200065