Interval total colorings of graphs
P.A. Petrosyan, A.Yu. Torosyan, N.A. Khachatryan

TL;DR
This paper studies interval total colorings of graphs, exploring their properties and determining the minimum and maximum number of colors needed for specific graph classes.
Contribution
It introduces the concept of interval total colorings and provides exact values for the range of colors for certain graph classes.
Findings
Characterization of interval total colorings
Exact values for minimum and maximum colors in specific graphs
Properties and bounds of interval total colorings
Abstract
A total coloring of a graph 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 \emph{interval total -coloring} of a graph is a total coloring of with colors such that at least one vertex or edge of is colored by , , and the edges incident to each vertex together with are colored by consecutive colors, where is the degree of the vertex in . In this paper we investigate some properties of interval total colorings. We also determine exact values of the least and the greatest possible number of colors in such colorings for some classes of graphs.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Limits and Structures in Graph Theory · Advanced Graph Theory Research
