Some structural, metric and convex properties of the boundary of a graph
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Let u;v be two vertices of a connected graph G . The vertex v is said to be a boundary vertex of u if no neighbor of v is further away from u than v . The boundary of a graph is the set of all its boundary vertices. In this work, we present a number of properties of the boundary of a graph under diÆerent points of view: (1) a realization theorem involving diÆerent types of boundary vertex sets: extreme set, periphery, contour, and the whole boundary; (2) the contour is a monophonic set; and (3) the cardinality of the boundary is an upper bound for both the metric dimension and the determining number of a graph
CitationHernando, M. [et al.]. Some structural, metric and convex properties of the boundary of a graph. "Ars combinatoria", 25 Abril 2013, vol. 109, p. 267-283.