On monophonic sets in graphs
نویسندگان
چکیده
In this paper we study monophonic sets in a connected graph G. First, we present a realization theorem proving, that there is no general relationship between monophonic and geodetic hull sets. Second, we study the contour of a graph, introduced by Cáceres and alt. [2] as a generalization of the set of extreme vertices where the authors proved that the contour of a graph is a g-hull set; in this work we show that the contour must also be monophonic. Finally, we focus our attention on the so-called edge Steiner sets. We prove that every edge Steiner set W in G is edge monophonic, i.e., every edge of G lies on some monophonic path joining two vertices of W .
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