Signed 2-independence of the Cartesian product of directed cycles
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A function f : V (D) → {−1; 1} defined on the vertices of a digraph D = (V (D);A(D)) is called a signed 2-independence function if f(N[v]) ≤ 1 for every v in Σ D. The weight of a signed 2-independence function is f(V (D)) = v2V (D) f(v). The signed 2-independence number of a digraph D, denoted by 2 s(D), equals the maximum weight of a signed 2-independence function on D. Let Cm × Cn be the Cartesian product of directed cycles Cm and Cn. In this paper, the exact values of 2 s(Cm × Cn) for 2 ≤ m ≤ 5 and n ≥ 2 are determined.
Abstract
A function f : V (D) → {−1; 1} defined on the vertices of a digraph D = (V (D);A(D)) is called a signed 2-independence function if f(N[v]) ≤ 1 for every v in Σ D. The weight of a signed 2-independence function is f(V (D)) = v2V (D) f(v). The signed 2-independence number of a digraph D, denoted by 2 s(D), equals the maximum weight of a signed 2-independence function on D. Let Cm × Cn be the Cartesian product of directed cycles Cm and Cn. In this paper, the exact values of 2 s(Cm × Cn) for 2 ≤ m ≤ 5 and n ≥ 2 are determined.
참고문헌 (7)
- G. Chartrand, "Graphs and digraphs" (2005), Chapman and Hall
- M.A. Henning, "Signed 2-independence in graphs", Discrete Math, 250, pp.93~107 (2002)
- R. Gallant, "Limited packing in graphs", Discrete Appl. Math, 158, pp.1357~1364 (2010)
- S.M. Hosseini Moghaddam, "O signed 2-independence number of graphs", Electronic Journal of Graph Theoty and Applications, 5(1), pp.36~42 (2017)
- E.F. Shan, "Upper bounds on signed 2-independence number of graphs", Ars Combin, 69, pp.229~239 (2003)
- L. Volkmann, "Signed 2-independence in digraphs", Discrete. Math, 312, pp.465~471 (2012)
- H.C. Wang, "Signed 2-independence of Cartesian product of directed paths", International Journal of Computer Mathematics, 91(6), pp.1190~1201 (2014)