A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimum cardinality of a geodetic set of G. We prove that it is NP complete to decide for a given chordal or chordal bipartite graph G and a given integer k whether G has a geodetic set of cardinality at most k. Furthermore...

The growing demand for dissemination of spatial data in the Web gives at the same time new challenges also for the problem of generalization. The Extensible Markup Language (XML) technology is widely regarded as a basis for general data processing in the Web. The Geographic Information (GI) community has also started adopting XML techniques for GI processing on the Web platform. Once XML-based ...

A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbor in D. A geodetic dominating set S is both a geodetic and a dominating set. The geodetic (domination, geodetic domination) number g(G)(γ(G), γg(G)) of G is...

For a nontrivial connected graph G = (V (G), E(G)), a set S ⊆ V (G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum order of its edge geodetic sets. Bounds for the edge geodetic number of Cartesian product graphs are proved and improved upper bounds are determined for a speci...

In past years, various cloaks have attracted the attention of many scientists but they usually remain confined to a single function. Cloaks combining multiple functions, however, are desirable. this paper, we design thermoelastic with dual functionality by coordinate transformation technique. The wave equations for cloaking and explicit expressions required material parameters established. Symm...

This paper outlines an algorithm for an Amorphous Computer [1] that causes each processor to assign itself a coordinate such that the resulting (logical) coordinate system maps approximately, under some affine transformation, to the physical coordinate system of the processors.

For a connected graph G of order n, a set S ⊆ V (G) is a geodetic set of G if each vertex v ∈ V (G) lies on a x-y geodesic for some elements x and y in S. The minimum cardinality of a geodetic set of G is defined as the geodetic number of G, denoted by g(G). A geodetic set of cardinality g(G) is called a g-set of G. A set S of vertices of a connected graph G is an open geodetic set of G if for ...