Two Tight Independent Set Conditions for Fractional (g, f, m)-Deleted Graphs Systems
- Gao, Wei 1
- García Guirao, Juan Luis 2
- Wu, Hualong 1
-
1
Yunnan Normal University
info
-
2
Universidad Politécnica de Cartagena
info
ISSN: 1575-5460
Año de publicación: 2018
Volumen: 17
Número: 1
Páginas: 231-243
Tipo: Artículo
Otras publicaciones en: Qualitative theory of dynamical systems
Resumen
A graph G is called a fractional (g, f, m)-deleted graph if the resulting graph admits a fractional (g, f)-factor after m edges are removed. An important fact in the characterization of a discrete graph dynamical system is played by the independent sets, i.e., subsets of the vertex set of G in which any two of them are not adjacent because they reflect the sparsity and stability of the graph system in somehow. The neighborhoods union of independent sets characterizes the local density and local clustering characteristics of the graph system. In this paper, we study the relationship between characteristics of independent sets and fractional (g, f, m)-deleted graph systems. The main contributions cover two aspects: first, we present an independent set degree condition for a graph to be fractional (g, f, m)-deleted; later an independent set neighborhood union condition for fractional (g, f, m)-deleted graphs is determined. Furthermore, we show that the results obtained are the best in some sense.
Información de financiación
Financiadores
-
MINECO
- MTM2014- 51891-P
-
Fundación Séneca de la Región de Murcia
- 19219/PI/14
-
National Natural Science Foundation of China
- 11401519
Referencias bibliográficas
- 1. Ackerman, J., Ayers, K., Beltran, E.J., Bonet, J., Lu, D., Rudelius, T.: A behavioral characterization of discrete time dynamical systems over directed graphs. Qual. Theory Dyn. Syst. 13, 161–180 (2014)
- 2. Aledo, J.A., Martinez, S., Valverde, J.C.: Parallel dynamical systems over graphs and related topics: a survey. J. Appl. Math. 2015 (2015) Article ID 594294. doi:10.1155/2015/594294
- 3. Bondy, J.A., Mutry, U.S.R.: Graph Theory. Springer, Berlin (2008)
- 4. Farahani, M.R., Jamil, M.K., Imran, M.: Vertex P Iv topological index of Titania carbon nanotubes TiO2(m, n). Appl. Math. Nonlinear Sci. 1, 175–182 (2016)
- 5. Gao, W., Farahani, M.R.: Degree-based indices computation for special chemical molecular structures using edge dividing method. Appl. Math. Nonlinear Sci. 1, 99–122 (2016)
- 6. Gao, W., Guo, Y., Wang, K.Y.: Ontology algorithm using singular value decomposition and applied in multidisciplinary. Cluster Comput. 19, 2201–2210 (2016)
- 7. Gao, W., Liang, L., Xu, T., Zhou, J.: Degree conditions for fractional (g, f, n , m)-critical deleted graphs and fractional ID-(g, f, m)-deleted graphs. Bull. Malays. Math. Sci. Soc. 39, 315–330 (2016)
- 8. Gao, W., Wang, W.: The eccentric connectivity polynomial of two classes of nanotubes. Chaos Solitons Fractals 89, 290–294 (2016)
- 9. Gao, W., Wang, W.: The fifth geometric arithmetic index of bridge graph and carbon nanocones. J. Differ. Equ. Appl. (2016). doi:10.1080/10236198.2016.1197214
- 10. Guirao, J.L.G., Luo, A.C.J.: New trends in nonlinear dynamics and chaoticity. Nonlinear Dyn. 84, 1–2 (2016)
- 11. Jin, J.: Multiple solutions of the Kirchhoff-type problem in RN. Appl. Math. Nonlinear Sci. 1, 229–238 (2016)
- 12. Zhou, S.: A sufficient condition for a graph to be an (a, b, k)-critical graph. J. Comput. Math. 87(10), 2202–2211 (2010)
- 13. Zhou, S., Bian, Q.: An existence theorem on fractional deleted graphs. Period. Math. Hung. 71, 125–133 (2015)
- 14. Zhou, S., Sun, Z., Xu, Y.: A theorem on fractional ID-(g, f )-factor-critical graphs. Contrib. Discrete Math. 10(2), 31–38 (2015)
- 15. Zhou, S., Sun, Z.: On all fractional (a, b, k)-critical graphs. Acta Math. Sin. Engl. Ser. 30(4), 696–702 (2014)
- 16. Zhou, S., Wu, J., Pan, Q.: A result on fractional ID-[a, b] -factor-critical graphs. Australas. J. Comb. 58, 172–177 (2014)
- 17. Zhou, S., Yang, F., Sun, Z.: A neighborhood condition for fractional ID-[a, b]-factor-critical graphs. Discuss. Math. Graph Theory 36(2), 409–418 (2016)