Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Let G1 and G2 be two simple graphs. The tensor product of G1 and G2, denoted by G1 × G2, has vertex set V (G1 × G2) = V (G1) × V (G2) and edge set E(G1 × G2) ={(u1, v1)(u2, v2) : u1u2 ∈ E(G1) and v1v2 ∈ E(G2)}. In this paper, we determine vulnerability parameters such as toughness, scattering number, integrity and tenacity of the tensor product of the graphs Kr(s) × Km(n) for r ≥ 3,m ≥ 3, s ≥ 1 and n ≥ 1, where Kr(s) denotes the complete r-partite graph in which each part has s vertices. Using the results obtained here the theorems proved in [Aygul Mamut, Elkin Vumar, Vertex Vulnerability Parameters of Kronecker Products of Complete Graphs, Information Processing Letters 106 (2008), 258–262] are obtained as corollaries.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
741--750
Opis fizyczny
Bibliogr. 10 poz., rys.
Twórcy
autor
- Department of Mathematics Annamalai University Annamalainagar – 608 002, India
autor
- Department of Mathematics Annamalai University Annamalainagar - 608 002, India
Bibliografia
- [1] A. Kirlangiç, A measure of graph vulnerability: scattering number, IJMMS 30 (2002),1–8.
- [2] A. Mamut, E. Vumar, Vertex vulnerability parameters of Kronecker products of complete graphs, Information Processing Letters 106 (2008), 258–262.
- [3] V. Aytaç, Computing the tenacity of some graphs, Selcuk J. Appl. Math. 10 (2009), 107–120.
- [4] K. Bagga, L. Beineke, W. Goddard, M. Lipman, R. Pippert, A survey of integrity, Discrete Appl. Math. 37/38 (1992), 13–28.
- [5] K. Bagga, L. Beineke, M. Lipman, R. Pippert, Edge-integrity a survey, Discrete Math. 124 (1994), 3–12.
- [6] R. Balakrishnan, K. Ranganathan, A text book of graph theory, Springer-Verlag, New York, 2000.
- [7] J.A. Bondy, U.S.R. Murty, Graph theory with applications, The Macmillan Press, London, 1976.
- [8] V. Chvàtal, Tough graphs and Hamiltonian circuits, Discrete Math. 5 (1973), 215–228.
- [9] M. Cozzens, D. Moazzami, S. Stuckle, The tenacity of a graph, [in:] Proc. Seventh International Conf. on the Theory and Application of Graphs, Wiley, New York, 1995, 1111–1122.
- [10] W. Imrich, S. Klavžar, Product Graphs: Structure and Recognition, Wiley, 2000.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-73138a76-bceb-4007-a8f9-314915141fec