2014/08/11 by Petros A. Petrosyan, Petrosyan, Petros A., Nerses A. Khachatryan +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1408.2317
17 pages
arxiv created 2014/08/11 · openalex publication_date 2014/08/11 · arxiv updated 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 obtain the same color. An interval total t-coloring of a graph G is a total coloring of G with colors 1,…,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. In this paper we prove that all complete multipartite graphs with the same number of vertices in each part are interval total colorable. Moreover, we also give some bounds for the minimum and the maximum span in interval total colorings of these graphs. Next, we investigate interval total colorings of hypercubes Qn. In particular, we prove that Qn (n≥ 3) has an interval total t-coloring if and only if n+1≤ t≤ ((n+1)(n+2))/(2).