| Online ISSN | : | 2953-7975 |
| Print ISSN | : | 1829-1740 |
Vol. 59 No. 2 (267) (2025)
Published:
2025-06-25
Mathematics
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Mathematics
ON SEMISTRONG EDGE-COLORINGS OF OUTERPLANAR GRAPHS
AbstractA matching M of a graph G is called semistrong, if every edge of M has a vertex of degree one in the induced subgraph by the vertices of M. A semistrong edge-coloring of a graph G is a proper edge-coloring in which every color class induces a semistrong matching. The minimum number of colors required for a semistrong edge-coloring is called the semistrong chromatic index of G and denoted by $\chi'_{ss}(G)$. In this paper, we propose a new approach for constructing semistrong edge-colorings and provide an upper bound on the semistrong chromatic index of outerplanar graphs.
ReferencesWest D.B. Introduction to Graph Theory. Prentice-Hall, New Jersey (2001). https://dwest.web.illinois.edu/igt/
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Fouquet J.L., Jolivet J.L. Strong Edge-Colorings of Graphs and Applications to Multi-k-Gons. Ars Combinatoria 16 (1983), 141-150.
Andersen L.D. The Strong Chromatic Index of a Cubic Graph is at Most 10. Discrete Math. 108 (1992), 231-252. https://doi.org/10.1016/0012-365X(92)90678-9
bibitem{horak}
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href{ https://doi.org/10.1002/jgt.3190170204}{ https://doi.org/10.1002/jgt.3190170204}
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Bruhn H., Joos F. A Stronger Bound for the Strong Chromatic Index. Combin., Probab. Comput. I 27 (2018), 21-43. https://doi.org/10.1016/j.endm.2015.06.038
Hurley Eoin, Rémi de Joannis de Verclos, Kang R.J. An Improved Procedure for Coloring Graphs of Bounded Local Density. Proc. of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics (2020), 135-148. https://doi.org/10.19086/aic.2022.7
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Mechanics
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Mechanics
LOADS TRANSFER FROM THE SYSTEMS OF FINITE NUMBER FINITE-LENGTH STRINGERS TO AN INFINITE SHEET THROUGH ADHESIVE LAYERS
AbstractThe article considers the problem for an elastic infinite plate (sheet), which along of two parallel lines of its upper surface is strengthened by systems of finite number finite-lenght stringers having different elastic properties. The interaction between infinite sheet and stringers take place through thin, uniform, elastic adhesive layers having other physical-mechanical properties and geometric configuration. The stringers are deformed under the action of horizontal concentrated forces, which are applied at one end points of stringers. The problem of determining unknown contact forces acting between infinite sheet and stringers is reduced to the system of Fredholm integral equations of second kind with respect to arbitrary finite number of unknown functions, which are specified along of two parallel lines on different finite intervals. Further, are determined of the change regions of the problem characteristic parameters, for which this system of integral equations allows the exact solution and which can be solved by the method of successive approximations. Some particular cases are considered and the character and behavior of unknown shear contact forces near the end points of the stringers are investigated. For these cases numerical results depending on the multiparameters of the problem are investigated in the previous article (A.V. Kerobyan, K.P. Sahakyan, Proc. YSU. Phys. Math. Sci. 57 (3) (2023), 86--100).
ReferencesKerobyan A.V., Sahakyan K.P. Transfer of Loads from Three Heterogeneous Elastic Stringers with Finite Lengths to an Infinite Sheet through Adhesive Layers. Proc. of the YSU A: Phys. Math. Sci. 57 (2023), 86-100. https://doi.org/10.46991/PYSU:A/2023.57.3.086
Kerobyan A.V. On a Problem for an Elastic Infinite Sheet Strengthened by Two Parallel Stringers with Finite Lengths through Adhesive Shear Layers. Proc. of the YSU A: Phys. Math. Sci. 54 (2020), 153-164. https://doi.org/10.46991/PYSU:A/2020.54.3.153
Kerobyan A.V. About Contact Problems for an Elastic Half-Plane and the Infinite Plate with Two Finite Elastic Overlays in the Presence of Shear Interlayers. Proc. of the YSU A: Phys. Math. Sci. 49 (2015), 30-38. https://doi.org/10.46991/PYSU:A/2015.49.2.030
Kerobyan A.V. Contact Problems for an Elastic Strip and the Infinite Plate with Two Finite Elastic Overlays in the Presence of Shear Interlayers.
Proc. NAS RA: Mechanics 67 (2014), 22-34 (in Russian). https://doi.org/10.33018/67.1.2
Grigoryan E.Kh., Kerobyan A.V., Shahinyan S.S. The Contact Problem for the Infinite Plate with Two Finite Stringers, One from which is Glued, Other is Ideal Conducted.
Proc. NAS RA: Mechanics 55 (2002), 14-23 (in Russian).
Lubkin J.I., Lewis L.C. Adhesive Shear Flow for an Axially Loaded, Finite Stringer Bonded to an Infinite Sheet. Quarterly Journal of Mechanics and Applied Mathematics XXIII (1970), 521-533. https://doi.org/10.1093/qjmam/23.4.521
Kerobyan A.V., Sarkisyan V.S. The Solution of the Problem for an Anisotropic Half-plane on the Boundary of which Finite Length Stringer is Glued. Proc. of the Scientific Conf., Dedicated to the 60th Anniversary of the Pedagogical Institute of Gyumri 1 (1994). Gyumri, Vysshaya Shkola, 73-76 (in Russian).
Grigoryan E.Kh. On Solution of Problem for an Elastic Infinite Plate, one the Surface of which Finite Length Stringer is Glued. Proc. NAS RA: Mechanics 53 (4) (2000), 11-16 (in Russian).
Sarkisyan V.S., Kerobyan A.V. On the Solution of the Problem for Anisotropic Half-plane on the Edge of which a Nonlinear Deformable Stringer of Finite Length is Glued. Proc. NAS RA: Mechanics 50 (1997), 17-26 (in Russian).
Kerobyan A.V., Sahakyan K.P. Loads Transfer from Finite Number Finite Stringers to an Elastic Half-plane through Adhesive Shear Layers. Proc. NAS RA: Mechanics 70 (2017), 39-56 (in Russian). https://doi.org/10.33018/70.3.4
Kerobyan A.V. Transfer of Loads from a Finite Number of Elastic Overlays with Finite Lengths to an Elastic Strip through Adhesive Shear Layers. Proc. of the YSU A: Phys. Math. Sci. 53, 109-118 (2019). https://doi.org/10.46991/PYSU:A/2019.53.2.109
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Muki R., Sternberg E. On the Diffusion of Load from a Transverse Tension Bar into a Semi-infinite Elastic Sheet. Transactions of the ASME (4) (1968), 737-746. https://doi.org/10.1115/1.3601299
Shilov G.E. Mathematical Analysis. Special Course. Moscow, State Publishing House of Physical and Mathematical Literature (1961), 442 (in Russian).
Grigolyuk E.I., Tolkachev V.M. Contact Problems of the Theory of Plates and Shells. Moscow, Mashinostroenie (1980), 416 (in Russian).
Aleksandrov B.M., Mkhitaryan S.M. Contact Problems for Bodies with Thin Coatings and Interlayers. Moscow, Nauka (1983), 488 (in Russian).
Sarkisyan V.S. Contact Problems for Semi-planes and Strips with Elastic Overlays. Yerevan, YSU Publ. (1983), 260 (in Russian).
