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Pawar, Madhukar M.
- 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
- B. Bollobas, Coloring lattices, Algebra Universalis, 7 (1977), 313-314.
- B. Bollobas and I. Rival, The maximal size of the covering graph of a lattice, Algebra Universalis, 9 (1979), 371-373.
- B. A. Davey and H. A. Priestley, Introduction to lattices and order, Cambridge University Press, 1990.
- N. D. Filipov, Comparability graphs of partially ordered sets of different types, Colloq. Math. Soc. Janos Bolyai, 33 (1980), 373-380
- G. Gratzer, General lattice theory , Academic press, New York, 1978.
- D. Kelley, and I. Rival, Crown, fences and dismantlable lattices, Canad. J. Math. 27 (1974), 636-665.
- S. K. Nimbhorkar, M. P.Wasadikar, and M.M. Pawar, Colorig of lattices, Math. Slovaca, 60(4) (2010), 419-434.
- A. Patil, B. N. Waphare, V. Joshi and H. Y. Pourali, Zero divisor graphs of lower dismantlable lattices-I, Math. Slovaca, (To appear).
- M. M. Pawar, Symmetricity and enumeration in posests, Ph.D. Thesis, North Maharashtra University, Jalgaon, 1999.
- I. Rival, Lattices with doubly irreducible elements, Canad. Math. Bull., 17 (1974), 91-95.
- N. K. Thakare, M. M. Pawar, and B. N. Waphare, A structure theorem for dismantlable lattices and enumeration, Period. Math. Hungarica 45(1-2) (2002), 147-160.
- D. B. West, Introduction to Graph Theory, Pearson Education, Inc., New Jersey, 2001.
- Covering Energy of Some Classes of Posets
Abstract Views :426 |
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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
- C. Adiga, A. Bayad, I. Gutman and S. A. Srinivas, The minimum covering energy of graph, Kragujcvac J. Sci., 34. (2012), 39–56.
- X. Chen and W. Xie, Energy of a hypercube and its compliment, Int. Jr. Algebra, 6(16) (2012), 799–805.
- D. Cvetkovi´c, M. Doob and H. Sachs, Spectra of Graphs Theory and Application, Academic Press, New York 1980.
- B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge Univ.Press, Cambridge 1990.
- G. Gr¨atzer, General Lattice Theory, Academic press, New York 1978.
- I. Gutman, The energy of graph, Ber. Math. Stat.Sekt. Forschungsz. Graz, 103 (1978), 1–22.
- I. Gutman and B. Furtula, The total π-electron energy saga, Croat. Chem. Acta 90 (2017) 359–368.
- I. Gutman and B. Furtula, Energies of Graphs - Survey, Census, Bibliography, Center for Scientific Research, Kragujevac, (2019) ISBN 978-86-81037-62-1
- E. H¨uckel, Quantetheoretische Beitrage zum Benzolproblem I. Dei Electronenkonfiguration des Benzolsund verwandter Verbindungen., Z. Phy., 70 (1931), 204–286.
- S. A. Mane and B. N. Waphare, Regular connected bipancyclic spanning subgraphs of hypercubes, Comput. Math. Appl., 62 (2011), 3551–3
- S. A. Mane and B. N. Waphare, On independent and (d, n)-domination numbers of hypercubes, AKCE Int. J. Graphs and Combi., 9(2) (2012), 161–168.
- M. M. Pawar and V. P. Bhamre, On Covering Energy of Posets, Math. Sc. Inter. Res.J. 4(2) (2015), 121–125.
- I. Rival, Lattices with doubly irreducible elements, Canad. Math. bull., 17 (1974), 91–95.
- N. K. Thakare, M. M. Pawar and B. N. Waphare, A structure theorem for dismantlable lattices and enumeration, Per. Math. Hung. 45(1-2) (2002), 147–160.
- W. T. Trotter, Combinatorics and Partially Ordered sets Dimension Theory, The Johns Hopkins Univ. Press, Baltimore and London 1992.
- D. B. West, Introduction to Graph Theory, (second edition), Pearson Education, Inc., New Jersey 2001.
- Jin Xu and Ruibin Qu, The Spectra of Hypercubes, J. Engg. Math., 16 (1999), 1–5.
- A Note on Isolate Domination Number of a Cubic Graph
Abstract Views :120 |
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Authors
Affiliations
1 Department of Engineering Sciences, Ramrao Adik Institute of Technology, D. Y. Patil Deemed to be University, Nerul, Navi Mumbai, 400706, IN
2 Department of Mathematics, S. S. V. P.S’s. Late Kr. Dr., P. R. Ghogrey Science College, Dhule- 424005, IN
1 Department of Engineering Sciences, Ramrao Adik Institute of Technology, D. Y. Patil Deemed to be University, Nerul, Navi Mumbai, 400706, IN
2 Department of Mathematics, S. S. V. P.S’s. Late Kr. Dr., P. R. Ghogrey Science College, Dhule- 424005, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 67-74Abstract
In this note we provide a solution to the problem “Find a structural characterization of cubic graph for which the isolate domination number equals one plus its domination number.” We show that if G is a cubic graph of order n and if 6 | n, then the isolate domination number of G is the same as the domination number of G. We also prove that if G is a connected cubic graph with diam(G) > 2, then the isolate domination number is the same as the domination number.Keywords
Domination Number, Isolate Domination Number, Total Domination Number, Cubic Graphs, Private Neighbour.References
- C. Berge, Theorie des graphes et ses applications, ,Collection Universitaire de Mathematiques, Dunod, Paris, 1958.
- C. Berge, Theory of Graphs and its Applications , Methuen, London, 1962.
- S. T. Bhangale and M. M. Pawar, Isolate and independent domination number of some classes of graphs , AKCE Int. J. of Graphs and Combinatorics, 16 (2019), 110–115.
- I. S. Hamid and S. Balamurugam, Isolate domination in graphs Arab J. Maths. Sci., 22 (2015), 232–241.
- F. Harary, Graph theory, Addison-Wesley Publishing Company, Inc 1969.
- M. A Henning and A. Yeo, Total Domination in Graphs Springer Monographs in Mathematics, 2013.
- O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ.,38 (Amer. math. Soc., Providence, RI) 1962.
- N. J. Rad, Some notes on isolate domination in graphs AKCE Int. J. Graphs and Combinatorics, 14 (2017), 112–117.
- D. B. West, Introduction to Graph Theory, (second edition), Pearson Education, Inc., New Jersey, 2001.