Author

# Seyed Mahmoud Sheikholeslami

Other affiliations: China University of Technology, Minjiang University, Azerbaijan University

Bio: Seyed Mahmoud Sheikholeslami is an academic researcher from Azarbaijan Shahid Madani University. The author has contributed to research in topics: Domination analysis & Vertex (graph theory). The author has an hindex of 19, co-authored 200 publications receiving 1380 citations. Previous affiliations of Seyed Mahmoud Sheikholeslami include China University of Technology & Minjiang University.

##### Papers published on a yearly basis

##### Papers

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TL;DR: This paper shows that for any connected graph G of order n>=3, @c"R(G)+@c (G)2@?n, where @c(G) is the domination number of G, and proves that the minimum and maximum values of |V"0|,|V"1|, •V"2| for a @ c"R-function f=(V" 0, V"1,V" 2) of a graph G?

83 citations

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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

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TL;DR: This work will present in two sections several variations of Roman dominating functions as well as the signifier functions of the Roman domination.

47 citations

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TL;DR: The study of the k-rainbow domatic number in graphs is initiated and some bounds for drk(G) are presented, where many of the known bounds of d( G) are immediate consequences of the results.

Abstract: For a positive integer k, a k-rainbow dominating function of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V (G) with f(v) = ∅ the condition ⋃ u∈N(v) f(u) = {1, 2, . . . , k} is fulfilled, where N(v) is the neighborhood of v. The 1-rainbow domination is the same as the ordinary domination. A set {f1, f2, . . . , fd} of k-rainbow dominating functions on G with the property that ∑ d i=1 |fi(v)| ≤ k for each v ∈ V (G), is called a k-rainbow dominating family (of functions) on G. The maximum number of functions in a krainbow dominating family on G is the k-rainbow domatic number of G, denoted by drk(G). Note that dr1(G) is the classical domatic number d(G). In this paper we initiate the study of the k-rainbow domatic number in graphs and we present some bounds for drk(G). Many of the known bounds of d(G) are immediate consequences of our results.

41 citations

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TL;DR: If G is a graph of order n and G ¯ is the complement of G, then for k ≥ 2 the Nordhaus–Gaddum inequality d r k ( G ) + d rk ( G ¯ ) ≤ n + 2 k − 2 .

34 citations

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

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28,685 citations

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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: 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

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HEC Montréal

^{1}TL;DR: In this paper, Nordhaus and Gaddum gave lower and upper bounds on the sum and product of the chromatic number of a graph and its complement, in terms of the order of the graph.

198 citations