Refine your search
Collections
Co-Authors
Year
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Pankaj,
- Order Prime Graphs of Finite Groups Un and K4
Abstract Views :222 |
PDF Views:5
Authors
Pankaj
1
Affiliations
1 Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502 Haryana, IN
1 Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502 Haryana, IN
Source
Research Journal of Science and Technology, Vol 9, No 2 (2017), Pagination: 285-287Abstract
We represent finite group in the form of graphs. These graphs are called order prime graphs. In this paper we shall study order prime graphs of finite groups Un (multiplicative group of integers modulo n) and K4 (Klein's four group).Keywords
Finite Group, Order Prime Graph.References
- Akbari S. and Mohammadian A., On zero divisor graphs of finite rings, J. Algebra, 2007; 314: 168-184.
- Anderson D.F. and Livingston P.S., The zero divisor graph of a commutative ring, J. Algebra, 1999; 217: 434-447.
- Beck I., Colouring of a commutative ring, J. Algebra, 1988; 116: 208-226.
- Birkhoff G. and Bartee T.C., Modern Applied Algebra, Mc-Graw Hill, New York, 1970.
- Bollobas B., Modern Graph Theory, Springer-Verlag, New York, 1998.
- DeMeyer F.R. and DeMeyer L., Zero Divisor Graphs of Semigroup, J. Algebra, 2005; 283: 190 β 198.
- Godase A. D., Unit Graph of Some Finite Group Zn, Cn and Dn, International Journal of Universal Science and Technology, 2015; 1(2): 122-130.
- Godase A. D., 2015, Unit Subgraph of Some Finite Group Zn, Cn and Dn, Research Gate pub. DOI:10.13140/RG.2.1.3415.6648
- Hall Marshall, Theory of Groups, The Macmillan Company, New York, 1961.
- Harary F., Graph Theory, Addison Wesley, Reading Mass, 1972.
- Herrnstein I.N., Topics in Algebra, Wiley Eastern Limited, 1975.
- Lang S., Algebra, Addison Wesley, 1967.
- Pankaj, Gunjan and Pruthi M., 2017, Unit Graphs and Subgraphs of Symmetric, Quaternion and Heisenberg Groups, Journal of Information and Optimization Sciences, 38(1), 207-2018.
- Pankaj, Unit Graphs and Subgraphs of Direct Product of Dihedral and Symmetric Groups, Arya Bhatta Journal of Mathematics and Informatics, 2017; 9(1): 59-70.
- Sattanathan M. and Kala R., An Introduction to Order Prime Graph, Int. J. Contemp. Math. Sciences, 2009; 4(10): 467 β 474.
- Smarandache Florentine, Special Algebraic Structures, in Collected Papers, Abaddaba, Oradea, 2000; 3: 78-81.
- Vasantha Kandasamy, W. B. and Singh S.V., Loops and their applications to proper edge colouring of the graph K2n, Algebra and its applications, edited by Tariq et al, Narosa Pub., 2001; 273-284.
- On The Properties of Generalized k-Pell Like Sequence
Abstract Views :384 |
PDF Views:0
Authors
Pankaj
1
Affiliations
1 Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502, Haryana, IN
1 Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502, Haryana, IN
Source
Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 656-662Abstract
The Pell sequence has been generalized in many ways, some by preserving the initial conditions, others by preserving the recurrence relation. In this paper, we define a new generalization {ππ,π}π=1β, with initial conditions ππ,0=2,ππ,1=π+2, which is generated by the recurrence relation ππ,π+1=2ππ,π+πππ,πβ1, for πβ₯1, where π,π are integer numbers. We produce an extended Binetβs formula for ππ,π and thereby the identities such as Catalanβs, Simpsonβs, dβ Ocageneβs etc.Keywords
k-Pell Sequence, k- Pell-Lucas Sequence, Recurrence Relation.References
- N. Bicknell, A primer on the Pell sequence and related sequence, The Fibonacci Quarterly, 13 (4) (1975), 345-349.
- A. Dasdemir, On the Pell, Pell-Lucas and Modified Pell Numbers by Matrix Method, Applied Mathematical Sciences, 5(64) (2011), 3173-3181.
- J. Ercolano, Matrix generators of Pell sequences, The Fibonacci Quarterly, 17 (1) (1979), 71-77.
- S. Halici, Some sums formulae for products of terms of Pell, Pell-Lucas and Modified Pell sequences, SAαΉΊ. Fen BillimleriDergisi, 15, Cilt, 2, SayΔ±, (2011), 151-155.
- A.F. Horadam, Applications of Modified Pell Numbers to Representations, Ulam Quarterly, 3 (1) (1994), 34-53.
- A. F. Horadam, Pell identities, The Fibonacci Quarterly, 9 (3) (1971), 245-252.
- P. Catarino, A note involving two-by-two matrices of the k-Pell and k-Pell-Lucas sequences, International Mathematical Forum, 8 (32) (2013), 1561-1568.
- P. Catarino, On Generating Matrices of the k-Pell-Lucas, k-Pell-Lucas and Modified k-Pell Sequences, Pure Mathematical Sciences, 3(2) (2014), 71 β 77.
- P. Catarino, On some identities and generating functions for k-Pell numbers, International Journal of Mathematical Analysis, 7 (38) (2013), 1877-1884.
- P. Catarino, P. Vasco, On some Identities and Generating Functions for k-Pell-Lucas sequence, Applied Mathematical Sciences, 7 (98) (2013), 4867-4873.
- P. Catarino, P. Vasco, Some basic properties and a two-by-two matrix involving the k-Pell Numbers, International Journal of Mathematical Analysis, 7 (45) (2013), 2209-2215.
- Pankaj, Some New Determinantal Identities of k-Pell Sequences, Journal of Combinatorics, Information & System Sciences (JCISS), 41(4) (2016), 207-213.
- K. Uslu, F. Yildirim, The Properties of Generalized k-Pell like Sequence using Matrices, Asian Journal of Applied Sciences, 4 (2) (2016), 453-457.
- A. Feng, Fibonacci identities via determinant of tridiagonal matrix, Applied Mathematics and Computation, 217 (2011), 5978-5981.
- S. Falcon, On the generating matrices of the k-Fibonacci numbers, Proyecciones Journal of Mathematics, 32 (4) (2013), 347-357.
- S. Falcon, and A. Plaza, On the k-Fibonacci numbers, Chaos, Solitons and Fractals, 5(32) (2007), 1615-1624.
- A. D. Godase, and M. B. Dhakne, On the Properties of Generalized k-Fibonacci like Sequence, Indian Journal in Number Theory, 1 (2014), 1-10.
- A. D. Godase, and M. B. Dhakne, On the Properties of Generalized k-Fibonacci like Sequence using Matrices, Indian Journal in Number Theory, 1 (2014), 11-16.
- A. D. Godase, Some New Properties for k-Fibonacci and k-Lucas Numbers using Matrix Methods, Researchgate Pub., (2015), DOI: 10.13140/RG.2.1.1734.6727.
- A. D. Godase, and M. B. Dhakne, On the properties of k-Fibonacci and k-Lucas numbers, International Journal of Advances in Applied Mathematics and Mechanics, 2(1) (2014), 100-106.
- A. D. Godase, and M. B. Dhakne, Summation Properties of Generalized k-Fibonacci like Sequence, Indian Journal in Number Theory, 1 (2015), 1-13.
- T. Koshy,Fibonacci and Lucas numbers with applications, Wiley-Intersection Pub.(2001).
- Pankaj, On the Properties of k-Jacobsthal and k-Jacobsthal-Lucas Numbers,The Journal Of The Indian Academy of Mathematics, 39(1) (2017), 49-58.
- S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and applications, Chichester: Ellis Horwood, 1989.