Boundary Sets

• Ignacio M. Pelayo
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

Let S be a set of vertices of a connected graph G = (V, E). The eccentricity e S (v) of a vertex vS is the maximum distance between v and any other vertex of S, i.e., e S (v) = max{d(v, u): uS}. A vertex uS is said to be a contour vertex of S if $$e_{S}(u) \geq e_{S}(v)$$ for every neighbor v of u in S. The set of all contour vertices of S is called the contour set of S and is denoted by Ct(S).

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