Arash Ahadi

Algorithmic complexity of proper labeling problems

A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The problem of proper labeling offers many variants and received a great interest during recent years. We consider the algorithmic complexity of some variants of the proper labeling problems, we present some polynomial time algorithms and NP-completeness results for them.

On the difference between chromatic number and dynamic chromatic number of graphs

Abstract A proper vertex k -coloring of a graph G is called dynamic , if there is no vertex v ∈ V ( G ) with d ( v ) ≥ 2 and all of its neighbors have the same color. The smallest integer k such that G has a k -dynamic coloring is called the dynamic chromatic number of G and denoted by χ 2 ( G ) . We say that v ∈ V ( G ) in a proper vertex coloring of G is a bad vertex if d ( v ) ≥ 2 and only one color appears in the neighbors of v . In this paper, we show that if G is a graph with the chromatic number at least 6 , then there exists a proper vertex χ ( G ) -coloring of G such that the set of bad vertices of G is an independent set. Also, we provide some upper bounds for χ 2 ( G ) − χ ( G ) in terms of some parameters of the graph G .

On the Complexity of Deciding Whether the Regular Number is at Most Two

The regular number of a graph

Algorithmic complexity of weakly semiregular partitioning and the representation number

G

Is there any polynomial upper bound for the universal labeling of graphs

G denoted by

Upper bounds for the 2-hued chromatic number of graphs in terms of the independence number

reg(G)