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Full-Text Articles in Physical Sciences and Mathematics
On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz
On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz
Theory and Applications of Graphs
Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets. The set chromatic number χs(G) of a graph G is the minimum number of colors required in a set coloring of G. In this work, we investigate a total analog of set colorings; that is, we study set colorings of the total graph of graphs. Given a graph G = (V, E) …