Papers by Omprakash Sikhwal
In this paper, we introduce a generalized bivariate Fibonacci-Like polynomials sequence, from whi... more In this paper, we introduce a generalized bivariate Fibonacci-Like polynomials sequence, from which specifying initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Also we define some properties of generalized bivariate Fibonacci-Like polynomials.
Generalized Identities on the Products of Fibonacci-Like and Lucas Numbers
The Fibonacci, Fibonacci-Like and Lucas sequences are shining stars in the vast array of integer ... more The Fibonacci, Fibonacci-Like and Lucas sequences are shining stars in the vast array of integer sequences. They have fascinated both amateurs and professional mathematicians for centuries. Also they continue to charm us with their beauty, their abundant applications and their ubiquitous habit of occurring in totally surprising and unrelated places. The product of Fibonacci number and Lucas number is a linear function of Fibonacci numbers. In this paper, we investigated some generalized identities on products of Fibonacci-Like and Lucas numbers. Further we showed that product is commutative when same location numbers will be taken in reverse order.
Third Order
A Dictionary of Devotions, 1993
Mobile AdHoc network is a collection of mobile hosts which is self-organized, self-maintained net... more Mobile AdHoc network is a collection of mobile hosts which is self-organized, self-maintained network. It forms a wireless network without any backbone infrastructure and centralized administration. Due to the lack of fixed infrastructure the control overhead increases in the network. The main objective of the paper is to reduce the control overhead in the network by using the domination set based routing. A node is a dominating node if it connects all other nodes in the network and the set of dominating nodes forms a domination set. This paper we propose a new routing technique for finding the route and reducing the reroute establishment delay. The effectiveness of the technique is demonstrated through simulation study using NS2. MSC 2010: 05C40, 05C69, 05C85, 05C99
Sum of Domination and Independence Numbers of Cubic Bipartite Graphs
The fastest growing area within graph theory is the study of domination and Independence numbers,... more The fastest growing area within graph theory is the study of domination and Independence numbers, the reason being its many and varied applications in such fields as social sciences, communications networks, algorithmic designs etc. A subset D of V is a dominating set of G if every vertex of V- D is adjacent to a vertex of D. The domination number of G, denoted by γ (G), is the minimum cardinality of a dominating set of G. Domination number is the cardinality of a minimum dominating set of a graph. Independence number is the maximal cardinality of an independent set of vertices of a graph. In this paper we present results on domination and independence numbers of cubic bipartite graphs.
Multiplicative Triple Fibonacci Sequences
Applied Mathematical Sciences, 2012
... Mamta Singh*, Shikha Bhatnagar** and Omprakash Sikhwal*** ... Much work has been done to stud... more ... Mamta Singh*, Shikha Bhatnagar** and Omprakash Sikhwal*** ... Much work has been done to study on Fibonacci-Triple sequences in additive form and the concept of Fibonacci-Triple sequences is first introduced by JZ Lee and JS Lee in 1987. ...
International …, 2010
In this paper we present common fixed point theorem for four expansive mappings in Menger spaces ... more In this paper we present common fixed point theorem for four expansive mappings in Menger spaces through semi and weak compatibility.
Multiplicative coupled Fibonacci sequences and some fundamental properties
Graph coloring is one of the most important concepts in graph theory and is used in many real tim... more Graph coloring is one of the most important concepts in graph theory and is used in many real time applications in engineering & science; various coloring methods are available and can be used on requirement basis. The proper coloring of a graph is the coloring of the vertices and edges with minimal number of colors such that no two vertices should have the same color. The minimum number of colors is called as the chromatic number and the graph is called properly colored graph. This paper present the importance of graph coloring in various fields.
On Second Order Additive Coupled Fibonacci Sequences
The coupled difference equations or recurrence relations involve two sequences of integers in whi... more The coupled difference equations or recurrence relations involve two sequences of integers in which the elements of one sequence are part of the generalization of the other, and vice versa. K. T. Atanassov was first introduced concept of additive coupled Fibonacci sequences in 1985. The coupled Fibonacci sequences are new direction of generalization of Fibonacci sequence. He defined four different schemes with properties of specific schemes for additive coupled Fibonacci sequences of second order. In this paper, we present some properties of additive coupled Fibonacci sequences of second order for real numbers.
On Fibonacci and Fibonacci-Like Numbers by Matrix Method
The Fibonacci, Lucas and Fibonacci-Like sequences are famous for possessing amazing properties an... more The Fibonacci, Lucas and Fibonacci-Like sequences are famous for possessing amazing properties and identities. There is a long tradition of using matrices and determinants to study Fibonacci numbers, Lucas numbers and other numbers of various celebrated sequences. In this paper, we present 2x2 order matrix representation of Fibonacci-Like numbers with some identities of Fibonacci-Like numbers and Fibonacci numbers. Sum of product of Fibonacci numbers and Fibonacci-Like numbers are taken in various pattern and identities derive by relevant matrix.
Some Identities for Even and Odd Fibonacci and Lucas Numbers
The Fibonacci sequence are well known and widely investigated. The Fibonacci and Lucas sequences ... more The Fibonacci sequence are well known and widely investigated. The Fibonacci and Lucas sequences have enjoyed a rich history. To this day, interest remains in the relation of such sequences to many fields. In this paper, we obtain some new properties for Fibonacci and Lucas numbers in terms of even and odd numbers, using Binet’s formula.
Determinantal Identities of Fibonacci, Lucas and Generalized Fibonacci-Lucas Sequence
Determinants have played a significant part in various areas in mathematics. For instance, they a... more Determinants have played a significant part in various areas in mathematics. For instance, they are quite useful in the analysis and solution of system of linear equations. There are different perspectives on the study of determinant. In this paper we present some determinant identities of generalized Fibonacci-Lucas sequence are presented.
Tamkang Journal of Mathematics, 2010
Fibonacci sequence stands as a kind of super sequence with fabulous properties. This note present... more Fibonacci sequence stands as a kind of super sequence with fabulous properties. This note presents Fibonacci-Triple sequences that may also be called 3-F sequences. This is the explosive development in the region of Fibonacci sequence. Our purpose of this paper is to demonstrate fundamental properties of Fibonacci-Triple sequence.
International Journal of Computer Applications, 2017
The coupled Fibonacci sequences are new direction of generalization of Fibonacci sequence. The co... more The coupled Fibonacci sequences are new direction of generalization of Fibonacci sequence. The concept of coupled Fibonacci sequence was first introduced by Atanassov, K. T. in 1985. He deliberated multiplicative coupled Fibonacci sequences of second order in 1995. Multiplicative coupled Fibonacci sequences are less known and popularized now days. Generalized Multiplicative Coupled Fibonacci sequences of second order are defined by the recurrence relations α n+2 = pβ n+1 qβ n and β n+2 = rα n+1 sα n , n ≥ 0 with initial conditions α 0 = a, β 0 = b, α
International Journal of Computer Applications, 2016
The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing p... more The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. Generalization of Fibonacci polynomial has been done using various approaches. One usually found in the literature that the generalization is done by varying the initial conditions. In this paper, Generalized Fibonacci polynomials are defined by W n (X)=XW n-1
Journal of Mathematical and Computational Science, Feb 15, 2014
Fibonacci numbers are fascinating and their impact on the field of mathematics has been great. In... more Fibonacci numbers are fascinating and their impact on the field of mathematics has been great. In this paper, mainly present formulas for the sums of k-Lucas numbers with indexes in an arithmetic sequence, say an r , for fixed integers a and r (0 1) ra . Also the generating function evaluates and presents the alternating sum for the k-Lucas numbers with arithmetic index.
Turkish Journal of Analysis and Number Theory, 2016
The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties a... more The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula n n-1 n-2 ,
Turkish Journal of Analysis and Number Theory, 2014
The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing p... more The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, some determinant identities of Fibonacci polynomials are describe. Entries of determinants are satisfying the recurrence relations of Fibonacci polynomials and Lucas polynomials.
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Papers by Omprakash Sikhwal