Dominator semi strong color partition in graphs
نویسندگان
چکیده
Let GG =(V,E)(V,E) be a simple graph. A subset SS is said to Semi-Strong if for every vertex vv in VV, |N(v)∩S|≤1|N(v)∩S|≤1, or no two vertices of have the same neighbour that is, are joined by path length VV. The minimum cardinality semi-strong partition called chromatic number and denoted χsGχsG. proper colour dominator dominates some class, , adjacent with element class. In this paper, instead partition, considered class partition.Several interesting results obtained.
منابع مشابه
Strong Alliances in Graphs
For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...
متن کاملOn Dominator Colorings in Graphs
Given a graph G, the dominator coloring problem seeks a proper coloring of G with the additional property that every vertex in the graph dominates an entire color class. We seek to minimize the number of color classes. We study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also show the relation between dominator chromatic number, chromat...
متن کاملOn the Strong Partition Dimension of Graphs
We present a new style of metric generator in graphs. Specifically we introduce a metric generator based on a partition of the vertex set of a graph. The sets of the partition will work as the elements which will uniquely determine the position of each single vertex of the graph. A set W of vertices of a connected graph G strongly resolves two different vertices x, y / ∈ W if either dG(x,W ) = ...
متن کاملAlgorithmic Aspects of Dominator Colorings in Graphs
In this paper we initiate a systematic study of a problem that has the flavor of two classical problems, namely Coloring and Domination, from the perspective of algorithms and complexity. A dominator coloring of a graph G is an assignment of colors to the vertices of G such that it is a proper coloring and every vertex dominates all the vertices of at least one color class. The minimum number o...
متن کاملDominator Coloring of Central Graphs
J. A. Bondy and U. S. R. Murty, Graph theory with Applications, London: MacMillan (1976). R. M. Gera, On Dominator Colorings in Graphs, Graph Theory Notes of New York LIT, 25-30 (2007) F. Harary, Graph Theory, Narosa Publishing 1969. D. Michalak, On Middle and Total graphs with Coarseness Number Equal 1, Lecture Notes in Mathematics, Volume 1018: Graph Theory, Springer-Verlag, Berlin, 139 – 150...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications Faculty of Sciences University of Ankara. Series A1: mathematics and statistics
سال: 2022
ISSN: ['1303-5991']
DOI: https://doi.org/10.31801/cfsuasmas.1014919