Characterization of Joined Graphs - Promsakon, C. (Communications in Mathematics and Applications, 2010)
The join of simple graphs G_1 and G_2, written by G_1G_2, is the graph obtained from the disjoint union between G_1 and G_2 by adding the edges {xy:xV(G_1),yV(G_2)}. We call a simple graph G as a joined graph if there are G_1 and G_2 that G=G_1G_2. In this paper, we give conditions to determine that which graphs are joined graphs and use its properties to investigate the chromatic number of joined graphs.