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Bhamre, Vandana P.
- Chromatic Classification of Dismantlable Lattices
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Authors
Affiliations
1 T. E. S's Smt. V. U. Patil Arts and Late Dr. B. S. Desale Science College, SAKRI Dist. Dhule 424304, IN
2 Department of Applied Science, Shri Gulabrao Deokar College of Engineering., Jalgaon 425002, IN
1 T. E. S's Smt. V. U. Patil Arts and Late Dr. B. S. Desale Science College, SAKRI Dist. Dhule 424304, IN
2 Department of Applied Science, Shri Gulabrao Deokar College of Engineering., Jalgaon 425002, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 3-4 (2016), Pagination: 329-335Abstract
A complete classification of the class of dismantlable lattices in terms of chromatic numbers is given. In fact, it is proved that a dismantlable lattice is at most 3-chromatic and the class of 2-Chromatic dismantlable lattices is characterized by using the structure theorem for dismantlable lattices.Keywords
Lattice, Dismantlable Lattice, Adjunct Operation, Covering Graph, Chromatic Number.
References
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- Covering Energy of Some Classes of Posets
Abstract Views :426 |
PDF Views:1
Authors
Affiliations
1 P. G. Dept. of Mathematics, S. S. V. P. S’s. Late Kr. Dr. P. R. Ghogrey Science College, Dhule, DHULE (M.S.) 424-005, IN
2 Department of Mathematics, Pratap College, Amalner, AMALNER, Dist. Jalgaon (M.S.) 425401, IN
1 P. G. Dept. of Mathematics, S. S. V. P. S’s. Late Kr. Dr. P. R. Ghogrey Science College, Dhule, DHULE (M.S.) 424-005, IN
2 Department of Mathematics, Pratap College, Amalner, AMALNER, Dist. Jalgaon (M.S.) 425401, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 3-4 (2020), Pagination: 193–205Abstract
The concept of the covering energy of a poset is introduced and its bounds are given. We compute covering energy of some classes of posets like Sn, 2n. The posets Dk and D'k are defined and two recurrence relations for the characteristic polynomials of these posets are obtained. The energies of the posets D1, D2, D3, D4 and D5 are explicitly computed. The existence of some eigenvalues for some type of Dk and D'k is proved.Keywords
Covering Energy of a Poset, Eigenvalues, Spectrum, Boolean Lattice, Diamond, Dk and D'kReferences
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