Author
Mustapha Chellali
Bio: Mustapha Chellali is an academic researcher from University of Blida. The author has contributed to research in topics: Domination analysis & Vertex (graph theory). The author has an hindex of 21, co-authored 130 publications receiving 1578 citations.
Papers published on a yearly basis
Papers
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TL;DR: This paper surveys results on k-domination and k-independence in graphs with positive integer k.
Abstract: In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of V − S is adjacent to at least k vertices in S The subset S is k-independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1 In this paper we survey results on k-domination and k-independence
140 citations
TL;DR: It is proved that equality between these two parameters holds for trees and cactus graphs with no even cycles, and that associated decision problem for Roman { 2 } -domination is NP-complete, even for bipartite graphs.
123 citations
TL;DR: First it is shown that the decision problem associated with γ d R ( G ) is NP-complete for bipartite and chordal graphs and some sharp bounds on the double Roman domination number are presented.
79 citations
Journal Article•
62 citations
TL;DR: This paper introduces two types of degrees, vertex–edge degree and edge–vertex degree, and studies their properties.
60 citations
Cited by
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TL;DR: The theory of graphs has broad and important applications, because so many things can be modeled by graphs, and various puzzles and games are solved easily if a little graph theory is applied.
Abstract: A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.
541 citations
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TL;DR: In this paper, the adjacency matrix, a matrix of O's and l's, is used to store a graph or digraph in a computer, and certain matrix operations are seen to correspond to digraph concepts.
Abstract: In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.
292 citations
TL;DR: This paper offers a survey of selected recent results on total domination in graphs and defines a set S of vertices in a graph G if every vertex of G is adjacent to some vertex in S.
289 citations
TL;DR: A survey of selected recent results on independent domination in graphs is offered and it is shown that not every vertex in S is adjacent to a vertex in S .
196 citations
TL;DR: This paper surveys results on k-domination and k-independence in graphs with positive integer k.
Abstract: In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of V − S is adjacent to at least k vertices in S The subset S is k-independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1 In this paper we survey results on k-domination and k-independence
140 citations