Browsing by Author "Swaminathan, V."
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Chromatic weak domatic partition in graphs
Aristotle, P.; Balamurugan, S.; Selva Lakshmi, P.; Swaminathan, V. (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
Sundareswaran, Raman; Swaminathan, V. (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 DIsets of G). This ... 
Distance majorization sets in graphs
Sundareswaran, Raman; Swaminathan, V. (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
Sundareswaran, Raman; Swaminathan, V. (Işık University Press, 20160630)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 ... 
Some results on the distance rbcoloring in graphs
Jothilakshmi, G.; Pushpalatha, A.P.; Suganthi, S.; Swaminathan, V. (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 rindependent sets is called a distance rcoloring. A study of distance rcoloring and distance rbcoloring ... 
Tight just excellent graphs
Mudartha, Irene Kulrekha; Sundareswaran, Raman; Swaminathan, V. (Işık University Press, 2019)A graph G is χexcellent if for every vertex v, there exists a chromatic partition π such that {v} ∈ π.A graph G is just χexcellent if every vertex appears as a singleton in exactly one χpartition. In this paper, a special ... 
Trivially extendable graphs
Angaleeswari, K.; Sumathi, P.; Swaminathan, V. (Işık University Press, 20150324)Let G be a simple graph. Let k be a positive integer. G is said to be kextendable 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 ...