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Search results for: geodesic measurements
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Weakly convex and convex domination numbers of some products of graphs
PublicationIf $G=(V,E)$ is a simple connected graph and $a,b\in V$, then a shortest $(a-b)$ path is called a $(u-v)$-{\it geodesic}. A set $X\subseteq V$ is called {\it weakly convex} in $G$ if for every two vertices $a,b\in X$ exists $(a-b)$- geodesic whose all vertices belong to $X$. A set $X$ is {\it convex} in $G$ if for every $a,b\in X$ all vertices from every $(a-b)$-geodesic belong to $X$. The {\it weakly convex domination number}...
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Photogrammetric and computerized report on site model in feasibility study of navigability channel on vistula spit
PublicationIn the report the authors present a course of geodesic and geo-computerized works upon realization of feasibility study of navigability channel on Vistula Spit. A procedure of acquiring verification and modeling of data for requirements of a numeric model of a bottom and site has been presented with construction of original software for 3D visualization of the Vistula Spit area. The activities described in the report can be...
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Weakly convex domination subdivision number of a graph
PublicationA set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...
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The convex domination subdivision number of a graph
PublicationLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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A Novel Approach of Using Selected Unconventional Geodesic Methods of Estimation on VTS Areas
PublicationThe Vessel Traffic Service (VTS) systems belong to the fundamental tools used in ensuring a high level of safety across sea basins with heavy traffic, where the presence of navigational hazards poses a great risk of collision or a ship running aground. In order to determine the mutual location of ships, VTS systems obtain information from different facilities, such as coastal radar stations, AIS, and vision systems. Fixing a ship’s...