Now showing items 1-7 of 7

• #### Chromatic weak domatic partition in graphs ﻿

(Işık University Press, 2019)
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 ...
• #### Integrity and domination integrity of gear graphs ﻿

(Işık University Press, 2016-06-30)
C.A. Barefoot, et. al.  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 ...
• #### Some results on the distance r-b-coloring in graphs ﻿

(Işık University Press, 2016)
Given a positive integer r, two vertices u, v ∈ V (G) are r- independent if d(u, v) > r. A partition of V (G) into r-independent sets is called a distance r-coloring. A study of distance r-coloring and distance r-b-coloring ...
• #### 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 ...
• #### Trivially extendable graphs ﻿

(Işık University Press, 2015-03-24)
Let G be a simple graph. Let k be a positive integer. G is said to be k-extendable if every independent set of cardinality k is contained in a maximum independent set of G. G is said to be trivially extendable if G is not ...