ON INTERVAL TOTAL COLORINGS OF BLOCK GRAPHS - Khachatryan, N.A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2015)
A total coloring of a graph G is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges get the same color. An interval total t-coloring of a graph G is a total coloring of G with colors 1,2, . . . ,t such that all colors are used and the edges incident to each vertex v together with v are colored by dG(v)+1 consecutive colors, where dg(v) is the degree of a vertex v in G. A block graph is a graph, in which every 2-connected component is a clique. In this paper we prove that all block graphs are interval total colorable. We also obtain some bounds for the smallest and greatest possible number of colors in interval total colorings of such graphs.