1. Detour convexity in graphs.
- Author
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Arco, R. L. and Canoy, Jr., S. R.
- Subjects
- *
CONVEX domains , *CONVEXITY spaces , *POINT set theory , *CALCULUS of variations , *CONVEX sets , *JOIN spaces , *SET theory - Abstract
Let G = (V (G),E(G)) be a connected graph. Given any two vertices u and v of G, the set ID[u, v] consists of all those vertices lying on a longest u-v path. A set S is a detour convex set if ID[u, v] ⊂ S for u, v ∈ S. The detour convexity number conD(G) of G is the maximum cardinality of a proper detour convex set of G. In this paper we characterize those graphs G having conD(G) = |V (G)| - 1. We also characterize the detour convex sets in the join K1 + G and the corona G H of graphs G and H. [ABSTRACT FROM AUTHOR]
- Published
- 2017