On the defining number and strong defining number for vertex colourings of Jahangir graphs
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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.
Abstract
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.
참고문헌 (13)
- H. Abdollahzadeh Ahangar, "On defining number of subdivided certain graph", Scientia Magna, 6(1), pp.110~120 (2010)
- J. C. Bermond, "Distributed loop computer networks: a survey", J. Parallel Distrib. Comput, 24, pp.2~10 (1995)
- D. Donovan, "Defining sets in combinatorics: A survey, In London Mathematical Society Lecture Note Series", pp.307~ (2003)
- W. A. Deuber, "The chromatic numbers of distance graphs", Discrete Math, 165, pp.195~204 (1997)
- A. D. Keedwell, "Critical sets for latin squares, graphs and block designs: a survey", Congr. Numer, 113, pp.231~245 (1996)
- E.S. Mahmoodian, "On defining numbers of vertex coloring of regular graphs", Discrete Math, 197, pp.543~554 (1999)
- E. S. Mahmoodian, "Defining sets of vertex coloring of graphs and latin rectangles", Discrete Math, 167, pp.451~460 (1997)
- E. Mendelsohn, "On defining spectrum of regular graph", Adv. Studies Contemp. Math
- D. A. Mojdeh, "Defining sets in (proper) vertex colorings of the Cartesian product of a cycle with a complete graph", Discuss. Math. Graph Theory, 26(1), pp.59~72 (2006)
- D. A. Mojdeh, "On Conjecture on the defining set of vertex graph coloring", Austral. J. Combin, 34, pp.153~160 (2006)
- D. A. Mojdeh, "On the defining number of (2n − 2)-vertex colorings of Kn × Kn", Bull. Iran Math. Soc, 31(1), pp.49~61 (2005)
- D. A. Mojdeh, "Defining sets in (proper) vertex colorings of Pm × Kn", Int. Math. Forum, 2(7), pp.321~327 (2007)
- D. B.West, "Introduction to graph theory (Second Edition)" (2001), Prentice Hall