Let G = (V, E) be a graph and u, v ~ V. Then, u strongly dominates v and v weakly dominates u if (i) uv ~ E and (ii) deg u >/deg v. A set D c V is a strong-dominating set (sd-set) of G if everyâ€¦ (More)

Let G = (V, E) be a graph. For a property P, let n(P) be the minimum number of sets into which V can be partitioned so that each set induces a subgraph H with property P. The number n(P) has beenâ€¦ (More)

Given an integer k â‰¥ 2, we consider vertex colorings of graphs in which no k-star subgraph Sk = K1,k is polychromatic. Equivalently, in a star-[k]-coloring the closed neighborhood N[v] of each vertexâ€¦ (More)

Let G be a vertex colored graph. The minimum number Ï‡(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of colorâ€¦ (More)

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The 3 -consecutive edge coloring number Ïˆâ€² 3c(G) of G is the maximum number ofâ€¦ (More)

A 3-consecutive C-coloring of a graph G = (V, E) is a mapping Ï† : V â†’ N such that every path on three vertices has at most two colors. We prove general estimates on the maximum number Ï‡Ì„3CC(G) ofâ€¦ (More)

For an integer k â‰¥ 1, the k-improper upper chromatic number Ï‡Ì„k-imp(G) of a graph G is introduced here as the maximum number of colors permitted to color the vertices of G such that, for any vertex vâ€¦ (More)