We give an inequality for the group chromatic number of a graph as an extension of Brooksâ€™ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality and discussâ€¦ (More)

A dynamic k-coloring of a graphG is a proper k-coloring of the vertices ofG such that every vertex of degree at least 2 in G will be adjacent to vertices with at least two different colors. Theâ€¦ (More)

For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent to vertices with atâ€¦ (More)

A proper vertex k-coloring of a graph G is dynamic if for every vertex v with degree at least 2, the neighbors of v receive at least two different colors. The smallest integer k such that G has aâ€¦ (More)

Given a graph G, for an integer c âˆˆ {2, . . . , |V (G)|}, define Î»c(G) = min{|X | : X âŠ† E(G), Ï‰(G âˆ’ X) â‰¥ c}. For a graph G and for an integer c = 1, 2, . . . , |V (G)| âˆ’ 1, define, Ï„c(G) = min XâŠ†E(G)â€¦ (More)

The vertex arboricity of graph G is the minimum number of colors that can be used to color the vertices of G so that each color class induces an acyclic subgraph of G. We prove results such as this:â€¦ (More)

Lai, H.-J., Graph whose edges are in small cycles, Discrete Mathematics 94 (1991) 11-22. Paulraja (1987) conjectured the following: (i) If every edge of a 2-connected graph G lies in a cycle ofâ€¦ (More)