###### The Ryjáček Closure and a Forbidden Subgraph

References [1] G. Chartrand, L. Lesniak and P. Zhang, Graphs & Digraphs (5th Ed.) (Chapman and Hall/CRC, Boca Raton, Florida, USA, 2010). [2] M. Jünger, W.R. Pulleyblank and G. Reinelt, On partitioning the edges of graphs into connected subgraphs, J. Graph Theory 9 (1985) 539-549. doi:10.1002/jgt.3190090416 [3] M. Las Vergnas, A note on matchings in graphs, Colloque sur la Théorie des Graphes, Cahiers Centre Études Rech. Opér. 17 (1975) 257-260. [4] M.M. Matthews and D.P. Sumner, Hamiltonian

###### Hamiltonicities of Double Domination Critical and Stable Claw-Free Graphs

R eferences [1] S. Ao, G. MacGillivray and J. Simmons, Hamiltonian properties of independent domination critical graphs , J. Combin. Math. Combin. Comput. 85 (2013) 107–128. [2] J. Brousek, Z. Ryjáček and O. Favaron, Forbidden subgraphs, Hamiltonicity and closure in claw-free graphs , Discrete Math. 196 (1999) 29–50. doi:10.1016/S0012-365X(98)00334-3 [3] V. Chvátal, Tough graphs and Hamiltonian circuits , Discrete Math. 306 (2006) 910–917 (reprinted from Discrete Math. 5 (1973) 215–228). doi:10.1016/j.disc.2006.03.011 [4] M

###### Heavy Subgraphs, Stability and Hamiltonicity

R eferences [1] P. Bedrossian, Forbidden Subgraph and Minimum Degree Conditons for Hamiltonicity (Ph.D. Thesis, Memphis State University, 1991). [2] P. Bedrossian, G. Chen and R.H. Schelp, A generalization of Fan’s condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness , Discrete Math. 115 (1993) 39–50. doi:10.1016/0012-365X(93)90476-A [3] L.W. Beineke, Characterizations of derived graphs , J. Combin. Theory Ser. B 9 (1970) 129–135. doi:10.1016/S0021-9800(70)80019-9 [4] J.A. Bondy and U.S.R. Murty, Graph Theory (GTM

###### Analysis of fractional factor system for data transmission in SDN

graph for every independent set I of G , a graph is a fractional independent-set-deletable ( a,b,m )-deleted graph (shortly, fractional ID-( a,b,m )-deleted graph). If a = b = k , then a fractional ID-( a,b,m )-deleted graph is a fractional ID-( k,m )-deleted graph. If m = 0, then a fractional ID-( a,b,m )-deleted graph is just a fractional ID-( a,b )-factor-critical graph. If G has a fractional ( g, f )-factor containing a Hamiltonian cycle, it is said that G includes a Hamiltonian fractional ( g, f )-factor. A graph G is called an ID-Hamiltonian

###### On k-Path Pancyclic Graphs

References [1] Y. Alavi and J.E. Williamson, Panconnected graphs, Studia Sci. Math. Hungar. 10 (1975) 19-22. [2] H.C. Chan, J.M. Chang, Y.L. Wang and S.J. Horng, Geodesic-pancyclic graphs, Discrete Appl. Math. 155 (2007) 1971-1978. [3] G. Chartrand, F. Fujie and P. Zhang, On an extension of an observation of Hamilton, J. Combin. Math. Combin. Comput., to appear. [4] G. Chartrand, A.M. Hobbs, H.A. Jung, S.F. Kapoor and C.St.J.A. Nash-Williams, The square of a block is Hamiltonian connected, J

###### An Implicit Weighted Degree Condition For Heavy Cycles

References [1] J.A. Bondy, Large cycles in graphs, Discrete Math. 1 (1971) 121-132. doi:10.1016/0012-365X(71)90019-7 [2] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan-London, Elsevier-New York, 1976). [3] V. Chvátal and P. Erdős, A note on hamiltonian circuits, Discrete Math. 2 (1972) 111-113. doi:10.1016/0012-365X(72)90079-9 [4] G.A. Dirac, Some theorems on abstract graphs, Proc. Lond. Math. Soc. 2 (1952) 69-81. [5] H. Enomoto, J. Fujisawa and K. Ota, A

######
Electronic Levels Of Cr^{2+} Ion Doped In II-VI Compounds Of ZnS – Crystal Field Treatment

## Abstract

The aim of present paper is to report the results on the modeling of the crystal field and spin-Hamiltonian parameters of Cr^{2+} doped in II-VI host matrix ZnS and simulate the energy levels scheme of such system taken into account the fine interactions entered in the Hamiltonian of the system. All considered types of such interaction are expected to give information on the new peculiarities of the absorption and emission bands, as well as of non-radiative transitions between the electronic states of impurity ions. The obtained results were disscused, compared with similar obtained results in literature and with experimental data.

###### Poisson and symplectic reductions of 4–DOF isotropic oscillators. The van der Waals system as benchmark

1 Introduction The use of computer algebra systems for normal forms computations is considered at present a routine operation. As a general reference see e.g. Sanders et al . [ 36 ] and Meyer et al . [ 32 ]. Nevertheless when we deal with special classes of differential equations, like Poisson or Hamiltonians systems which is our case, it is advisable to employ specific transformations as well as tailored variables for those problems [ 32 ], mostly connected with the symmetries that those systems might possess. More precisely we are interested in

###### Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems

. J. (2000). Portcontrolled Hamiltonian representation of distributed parameter systems, in N. E. Leonard and R. Ortega (Eds.), Proceedings of the IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Princeton, NJ, USA , pp. 28-38. Moore, R. E. (1964). Error in Digital Computation, the Automatic Analysis and Control of Error , John Wiley & Sons, New York, NY. Nedialkov, N. S. (2007). Interval tools for ODEs and DAEs, CD-Proceedings of the 12th GAMM-IMACS International Symposium on

###### Some Properties of The Solution of The Ramsey Model

Economic Studies, 35, 155 - 174. Mehlum ,H. (2005). A closed form Ramsey saddle path. The B.E. Journal of Macroeconomics (Contributions), 5 (1), Article 2. doi:10.2202/1534-6005.1267 Naz, R., Mahomed, F. M., & Chaudhry, A. (2014). A partial Hamiltonian approach for current value Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulations, 19(10), 3600-3610. doi:10.1016/j.cnsns.2014.03.023 Ramsey, F. P., (1928). A mathematical theory of savings. Economic Journal, 38, 543 - 559. Smith, W