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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Neighborhood-Restricted Achromatic Colorings Of Graphs, James D. Chandler Sr.
Neighborhood-Restricted Achromatic Colorings Of Graphs, James D. Chandler Sr.
Electronic Theses and Dissertations
A (closed) neighborhood-restricted 2-achromatic-coloring of a graph G is an assignment of colors to the vertices of G such that no more than two colors are assigned in any closed neighborhood. In other words, for every vertex v in G, the vertex v and its neighbors are in at most two different color classes. The 2-achromatic number is defined as the maximum number of colors in any 2-achromatic-coloring of G. We study the 2-achromatic number. In particular, we improve a known upper bound and characterize the extremal graphs for some other known bounds.
Global Supply Sets In Graphs, Christian G. Moore
Global Supply Sets In Graphs, Christian G. Moore
Electronic Theses and Dissertations
For a graph G=(V,E), a set S⊆V is a global supply set if every vertex v∈V\S has at least one neighbor, say u, in S such that u has at least as many neighbors in S as v has in V \S. The global supply number is the minimum cardinality of a global supply set, denoted γgs (G). We introduce global supply sets and determine the global supply number for selected families of graphs. Also, we give bounds on the global supply number for general graphs, trees, and grid graphs.