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RISS 인기검색어
- 검색키워드
- 저자 : N.D. Soner (검색결과 8 건)
- 무료
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- 유료
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ANWAR ALWARDI,N. D. Soner 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.1
Let G be a graph and u,v be any vertices of G. Then u and v are said to be P3-adjacent vertices of G if there is a subgraph of G, isomorphic to P3, Containing u and v. A P3-dominating set of G is a set D of vertices such that every vertex of G belongs to D or is P3-adjacent to a vertex of D. The P3-domination number of G denoted by P3 (G) is the minimum cardinality among the P3-dominating sets of vertices of G. In this paper we introduce and study the P3-domination of a graph G and analogous to this concept we define the P3-independence number P3 (G), P3-neighbourhood number P3 (G) and P3-domatic number dP3 (G). Some bounds and interesting results are obtained. Also the P3-adjacency motivated us to define new graphs in particular P3-neighbourhood graph, P3-complete graph, P3-regular graph, P3-complement graph and P3-complementary graph, some basic properties of these graphs are introduce and new method to construct any r-regular graph is established. finally we generalize the domination of graphs.
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Restrained edge domination number in graphs
S. Ghobadi,N. D. Soner 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
Let G = (V,E) be a graph. A set D ⊆ E is a restrained edge dominating set if every edge in E − D is adjacent to an edge in D and another edge in E − D. The restrained edge domination number of G, denoted by [수식](G), is the smallest cardinality of a restrained edge dominating set of G. The maximum order of a partition of E into restrained edge dominating sets of G is called the restrained edge domatic number of G and denoted by [수식](G). In this paper we determine restrained edge domination and restrained edge domatic number for certain classes of graphs and obtain some bounds for [수식] (G) and [수식](G). Finally, we construct a special class of restrained edge domatically full graphs.
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Inverse dominating set in fuzzy graphs
S. Ghobadi,N. D. Soner,Q. M. Mahyoub 장전수학회 2008 Proceedings of the Jangjeon mathematical society Vol.11 No.1
Let G be a graph with p vertices and let D be a minimum dominating set of G. If V −D contains a dominating set D' of G, then D' is called an inverse dominating set of G with respect to D. The inverse domination number γ(G) of G is the cardinality of a smallest inverse dominating set of G. This concept was introduced and studied by Kulli and Domke in [4] and [2] respectively. In this paper we introduce the concept of inverse dominating set in fuzzy graphs and obtain some bounds for the inverse domination number γ(G). Also we investigate the relationship of γ(G) with the other known parameters. Moreover, we also obtain Nordhaus- Gaddum type results for this parameter.
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A. M. Naji,N. D. Soner 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.2
For a graph G(V,E), a subset D of vertices of G is called a monopoly set of G if for every vertex v ∈ V - D has at least d(v) / 2 neighbors in D. The monopoly size of G is the smallest cardinality of a monopoly set in G, denoted by mo(G). In this paper, we investigate the relationship between monopoly size of graphs and some other parameters of a graph namely domination number (G) and k-dominating number k(G). Bounds on monopoly size of graphs in terms maximum degree, minimum degree, diameter, algebraic connectivity and Laplacian spectral radius of a graph are found.
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On the defining number and strong defining number for vertex colourings of Jahangir graphs
Z. Tahmasbzadehbaee,N.D. Soner 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.3
In a given graph G = (V,E), a set S of vertices with an assignment of colours to them is called a defining set for vertex colourings of G, if there exists a unique extension of the colours of S to a k ≥ χ(G) colouring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G, k). In this article,we study the chromatic number, the defining number and the strong defining number of the Jahangir graphs Jm,n.
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Further results on the common neighbourhood domination and some related graphs
A. Alwardi,N. D. Soner 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.1
In this paper we obtain some results and bounds on the common neighbourhood domination number (CN-domination number) of a graph G. Also we introduce the common neighbourhood domatic number (CN-domatic number). Common neighbourhood connectedness(CN-connectedness), Common neighbourhood regularity (CN-regularity), Common neighbourhood completeness (CN-completeness) are introduce by define the CN-connected graph, CN-regular graph, CN-complete garph and CN-complement. Some properties and interesting results of these graphs are established.
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Totally connected domination in graphs
ANWAR ALWARDI,N. D. Soner 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.4
In the last 50 years, Graph theory has seen an explosive growth due to interaction with areas like computer science, electrical and communication engineering, Operations Research etc. Perhaps the fastest growing area within graph theory is the study of domination, the reason being its many and varied applications in such fields as social sciences, communication networks, algorithm designs, computational complexity etc. There are several types of domination depending upon the nature of domination and the nature of the dominating set. In this paper, we introduce the totally connected domination in graphs in connected graphs, exact value for some standard graphs, bounds and some results are established
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TOPOLOGICAL PROPERTIES OF GRAPHENE USING ψk- POLYNOMIAL
AMMAR ALSINAI,ANWAR ALWARDI,N.D.SONER 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.3
Graphene is a two-dimensional material consisting of a single layer of carbon atom arranged in a honeycomb structure. Graphine exhibits important intrinsic properties such as high strength, excellent conductor of heat and electricity. In this research, k-polynomial, when k = 2 for the line graph of Graphene is established, the degree-based topological indices, such as first, second and third leap Zagreb indices are obtained. Accordingly, by using the derivative of 2- polynomial of Graphene the first, second leap hyper-Zagreb indices, and leap forgotten topological index of Graphene, are found.
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