Now showing items 1-6 of 6

• #### Chromatic weak domatic partition in graphs ﻿

In a simple graph G, a subset D of V (G) is called a chromatic weak dominating set if D is a weak dominating set and χ(< D >) = χ(G). Similar to domatic partition, chromatic weak domatic partition can be defined. The maximum ...
• #### Computational complexity of domination integrity in graphs ﻿

(Işık University Press, 2015)
In a graph G, those dominating sets S which give minimum value for |S| + m(G−S), where m(G−S) denotes the maximum order of a component of G−S, are called dominating integrity sets of G (briefly called DI-sets of G). This ...
• #### Distance majorization sets in graphs ﻿

(Işık University Press, 2015)
Let G = (V, E) be a simple graph. A subset D of V (G) is said to be a distance majorization set (or dm - set) if for every vertex u ∈ V − D, there exists a vertex v ∈ D such that d(u, v) ≥ deg(u) + deg(v). The minimum ...
• #### Global color class domination partition of a graph ﻿

(Işık University Press, 2019)
Color class domination partition was suggested by E. Sampathkumar and it was studied in [1]. A proper color partition of a finite, simple graph G is called a color class domination partition (or cd-partition) if every color ...
• #### Integrity and domination integrity of gear graphs ﻿

(Işık University Press, 2016-06-30)
C.A. Barefoot, et. al. [4] introduced the concept of the integrity of a graph. It is an useful measure of vulnerability and it is defined as follows. I(G) = min{|S| + m(G − S) : S ⊂ V (G)}, where m(G − S) denotes the order ...
• #### Tight just excellent graphs ﻿

A graph G is χ-excellent if for every vertex v, there exists a chromatic partition π such that {v} ∈ π.A graph G is just χ-excellent if every vertex appears as a singleton in exactly one χ-partition. In this paper, a special ...