Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture
In this study, from a tree with a quasi-spanning face, the algorithm will route Hamiltonian cycles. Goodey pioneered the idea of holding facing 4 to 6 sides of a graph concurrently. Similarly, in the three connected cubic planar graphs with two-colored faces, the vertex is incident to one blue and t...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1618498 |
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| author | T. Anuradha T. Lakshmi Surekha Praveena Nuthakki Bullarao Domathoti Ganesh Ghorai Faria Ahmed Shami |
| author_facet | T. Anuradha T. Lakshmi Surekha Praveena Nuthakki Bullarao Domathoti Ganesh Ghorai Faria Ahmed Shami |
| author_sort | T. Anuradha |
| collection | DOAJ |
| description | In this study, from a tree with a quasi-spanning face, the algorithm will route Hamiltonian cycles. Goodey pioneered the idea of holding facing 4 to 6 sides of a graph concurrently. Similarly, in the three connected cubic planar graphs with two-colored faces, the vertex is incident to one blue and two red faces. As a result, all red-colored faces must gain 4 to 6 sides, while all obscure-colored faces must consume 3 to 5 sides. The proposed routing approach reduces the constriction of all vertex colors and the suitable quasi-spanning tree of faces. The presented algorithm demonstrates that the spanning tree parity will determine the arbitrary face based on an even degree. As a result, when the Lemmas 1 and 2 theorems are compared, the greedy routing method of Hamiltonian cycle faces generates valuable output from a quasi-spanning tree. In graph idea, a dominating set for a graph S=V,E is a subset D of V. The range of vertices in the smallest dominating set for S is the domination number (S). Vizing’s conjecture from 1968 proves that the Cartesian fabricated from graphs domination variety is at least as big as their domination numbers production. Proceeding this work, the Vizing’s conjecture states that for each pair of graphs S,L. |
| format | Article |
| id | doaj-art-3cd6d9478fca4219bfd5b1e758797fb2 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3cd6d9478fca4219bfd5b1e758797fb22025-02-03T01:24:10ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1618498Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing ConjectureT. Anuradha0T. Lakshmi Surekha1Praveena Nuthakki2Bullarao Domathoti3Ganesh Ghorai4Faria Ahmed Shami5Department of Information TechnologyDepartment of Information TechnologyDepartment of Information TechnologyDepartment of Computer Science and EngineeringDepartment of Applied Mathematics with Oceanology and Computer ProgrammingDepartment of MathematicsIn this study, from a tree with a quasi-spanning face, the algorithm will route Hamiltonian cycles. Goodey pioneered the idea of holding facing 4 to 6 sides of a graph concurrently. Similarly, in the three connected cubic planar graphs with two-colored faces, the vertex is incident to one blue and two red faces. As a result, all red-colored faces must gain 4 to 6 sides, while all obscure-colored faces must consume 3 to 5 sides. The proposed routing approach reduces the constriction of all vertex colors and the suitable quasi-spanning tree of faces. The presented algorithm demonstrates that the spanning tree parity will determine the arbitrary face based on an even degree. As a result, when the Lemmas 1 and 2 theorems are compared, the greedy routing method of Hamiltonian cycle faces generates valuable output from a quasi-spanning tree. In graph idea, a dominating set for a graph S=V,E is a subset D of V. The range of vertices in the smallest dominating set for S is the domination number (S). Vizing’s conjecture from 1968 proves that the Cartesian fabricated from graphs domination variety is at least as big as their domination numbers production. Proceeding this work, the Vizing’s conjecture states that for each pair of graphs S,L.http://dx.doi.org/10.1155/2022/1618498 |
| spellingShingle | T. Anuradha T. Lakshmi Surekha Praveena Nuthakki Bullarao Domathoti Ganesh Ghorai Faria Ahmed Shami Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture Journal of Mathematics |
| title | Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture |
| title_full | Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture |
| title_fullStr | Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture |
| title_full_unstemmed | Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture |
| title_short | Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture |
| title_sort | graph theory algorithms of hamiltonian cycle from quasi spanning tree and domination based on vizing conjecture |
| url | http://dx.doi.org/10.1155/2022/1618498 |
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