Minimum 3-geodetically connected graphs
نویسندگان
چکیده
منابع مشابه
Some special minimum k-geodetically connected graphs
A connected graph G is k-geodetically connected (k-GC) if the removal of less than k vertices does not affect the distances (lengths of the shortest paths) between any pair of the remaining vertices. As such graphs have important applications in robust system designs, we are interested in theminimumnumber of edges required tomake a k-GC graph of order n, and characterizing those minimum k-GC gr...
متن کاملThe Recognition of Geodetically Connected Graphs 1
Let G = (V;E) be a graph with vertex set V of size n and edge set E of size m. A vertex v 2 V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hingefree graph. In general, a graph G is k-geodetically connected or k-GC for short if G can tolerate any k 1 vertices failures without increasing the distance among...
متن کاملThe Recognition of Geodetically Connected Graphs
Let G = (V; E) be a graph with vertex set V of size n and edge set E of size m. A vertex v 2 V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hinge-free graph. In general, a graph G is k-geodetically connected or k-GC for short if G can tolerate any k ?1 vertices failures without increasing the distance am...
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A convex drawing of a plane graph G is a plane drawing of G, where each vertex is drawn as a point, each edge is drawn as a straight line segment and each face is drawn as a convex polygon. A maximal segment is a drawing of a maximal set of edges that form a straight line segment. A minimum-segment convex drawing of G is a convex drawing of G where the number of maximal segments is the minimum ...
متن کاملOn 3*-connected graphs
Menger's Theorem states that in a 3-connected graph, any two vertices are joined by three openly disjoint paths. Here we consider 3-connected cubic graphs where two vertices exist so that the three disjoint paths between them contain all of the vertices of the graph (we call these graphs 3*connected); and also where the latter is true for ALL pairs of vertices (globally 3*-connected). A necessa...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2003
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(02)00591-7