Autor: Sahul Hamid, Ismail

Skocz do pozycji: 1.

Tytuł:: Global dominated coloring of graphs
Autorzy:: Kalarkop, David A.
Sahul Hamid, Ismail
Chellali, Mustapha
Rangarajan, R.
Tematy:: global dominated coloring
dominated coloring
dominated chromatic number; Pokaż więcej
Data publikacji:: 2024
Powiązania:: https://bibliotekanauki.pl/articles/59945806.pdf Link otwiera się w nowym oknie
Źródło:: Discussiones Mathematicae Graph Theory; 2024, 44, 4; 1293-1309
2083-5892
Opis:: In this paper, we initiate a study of global dominated coloring of graphs as a variation of dominated colorings. A global dominated coloring of a graph $G$ {is a proper coloring such that for each color class there are at least two vertices, one of which is adjacent to all the vertices of this class while the other one is not adjacent to any vertex of the class. The global dominated chromatic number of $G$ is the minimum number of colors used among all global dominated colorings of $G.$ In this paper, we establish various bounds on the global dominated chromatic number of a graph in terms of some graph invariants including the order, dominated chromatic number, domination number and total domination number. Moreover, characterizations of extremal graphs attaining some of these bounds are provided.} We also discuss the global dominated coloring in trees and split graphs.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Global Dominator Coloring of Graphs
Autorzy:: Hamid, Ismail Sahul
Rajeswari, Malairaj
Tematy:: global domination
coloring
global dominator coloring
dominator coloring; Pokaż więcej
Data publikacji:: 2019-05-01
Powiązania:: https://bibliotekanauki.pl/articles/31343452.pdf Link otwiera się w nowym oknie
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 2; 325-339
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Opis:: Let S ⊆ V. A vertex v ∈ V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let C = (V1, V2, . . ., Vk) be a coloring of G and let v ∈ V (G). A color class Vi is called a dom-color class or an anti domcolor class of the vertex v according as v is a dominator of Vi or an antidominator of Vi. The coloring C is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti dom-color class in C. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by χgd(G). This paper initiates a study on this notion of global dominator coloring.
Dostawca treści:: Biblioteka Nauki

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