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Full-Text Articles in Physical Sciences and Mathematics
Properties Of Small Ordered Graphs Whose Vertices Are Weighted By Their Degree, Constance M. Blalock
Properties Of Small Ordered Graphs Whose Vertices Are Weighted By Their Degree, Constance M. Blalock
Electronic Theses and Dissertations
Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standard graphical measures to incorporate these vertex weights. In particular, we designate the degree of each vertex as its weight. Previous research has not investigated weighting vertices by degree. We find the vertex weighted domination number in connected graphs, beginning with trees, and we define how weighted vertices can affect …
Bipartitions Based On Degree Constraints, Pamela I. Delgado
Bipartitions Based On Degree Constraints, Pamela I. Delgado
Electronic Theses and Dissertations
For a graph G = (V,E), we consider a bipartition {V1,V2} of the vertex set V by placing constraints on the vertices as follows. For every vertex v in Vi, we place a constraint on the number of neighbors v has in Vi and a constraint on the number of neighbors it has in V3-i. Using three values, namely 0 (no neighbors are allowed), 1 (at least one neighbor is required), and X (any number of neighbors are allowed) for each of the four constraints, results in 27 distinct types of …