Now showing items 1-5 of 5

• #### 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 ...
• #### On zagreb indices of double vertex graphs ﻿

Let G = (V, E) be a graph with at least 2 vertices, then the double vertex graph U₂(G) is the graph whose vertex set consists of all 2-subsets of V such that two distinct vertices {x, y} and {u, v} are adjacent if and only ...
• #### 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 ...