Weighted graphs in graph theory are created by weighing different values depending on the importance of connections or centers in a graph model. Networks can be modeled with graphs such that the devices and centers correspond to the vertices and connections correspond to the edges. In these ...
Weighted Graphs in Graph Theory - Explore the concept of weighted graphs in graph theory, their properties, and applications in various fields.
We note that we can express the Laplacian matrix via its linear operator, i.e., L=Lw [28], where w∈Rp(p−1)/2 is the vectorized form of the upper triangular part of the adjacency matrix, also known as the vector of graph weights. In addition, for connected graphs, it follows ...
ugh weighted graphs Facets of the linear ordering polytope: A unification for the fence family through weighted graphsFacets of the linear ordering polytope: A unification for the fence family through weighted graphsTheoretical or Mathematical/ graph theory...
Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory two methods of partitioning V are examined. In one method, partitionings of V are obtained by selecting threshold values and applying them to a maximal weighted spanning forest. In another method a ...
graph theory (Beasley1987; Beasley and Chu1996; Haynes et al.1998; Caprara et al.2000; Tutte and Tutte2001). In particular, domination in graphs is an important research area in graph optimization. It is difficult to say when the study of domination in graphs began, but we can say that...
and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present anO(nlognlog (nwmax))-time algorithm to compute an optimal bandwidth layout, wherenis the total number of vertices in the graph andwmaxis the maximum edge wei...
The network comparison comes from the graph comparison in graph theory. Early graph comparison methods, such as graph isomorphism21,22 and edit distance23,24,25, are mainly based on graph matching26 technology to decide whether two graphs are identical. Generally, the algorithms have the time com...
Our results also apply in some cases to arbitrary finite metric spaces, because any finite metric space has a corresponding minimal graph generated by taking a weighted complete graph and removing all extra edges. Other weighted graphs may also be constructed for a given finite metric space, and...
Parameterized algorithm Weighted graph problem Vertex cover 3-Hitting set Edge dominating set 1. Introduction Many fundamental problems in graph theory are NP-hard already on unweighted graphs. This wide class includes, among others, Vertex Cover, 3-Hitting Set, Edge Dominating Set and Max Internal...