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Independent Transversal Dominating Energy of a Graph
R. Rangarajan,D. Soner Nandappa,Raghu. V. D. 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
Let G be a simple graph and let V (G) be its vertex set. The independent transversal dominating set or γit-set is a dominating set of G which intersects every maximal independent set of G. Using the γit-set, a diagonal matrix is constructed which is similar to the ones available in the literature for covering set, equitable dominating set and so on. Using the idea of signless Laplacian, one can add this diagonal matrix to the usual adjacency matrix of G to obtain new matrix called independent transversal dominating adjacency matrix denoted by Ait(G). The sum of all the absolute values of eigenvalues of Ait(G) is called independent transversal dominating energy denoted by Eit(G). In the present paper, some spectral properties of Ait(G) are obtained. Some upper and lower bounds for the largest eigenvalue of Ait(G) and Eit(G) are derived. Eit(G) is obtained for some standard graphs.
Four orthogonal polynomials connected to a regular C-fraction with co-efficients as natural numbers
R. Rangarajan,P. Shashikala 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.4
In the present paper, four orthogonal polynomials are extracted from numerator as well as denominator polynomials of both even and odd order convergents of a regular C-fraction with co-effcients as natural numbers connected to Pade approximants. The two orthogonal polynomials extracted from denominators are shown to be classical othogonal polynomials and two orthogonal polynomials extracted from numerator are shown to be non-classical orthogonal polynomials.
Notions of balance in symmetric n-sigraphs
R. Rangarajan,P. Siva Kota Reddy 장전수학회 2008 Proceedings of the Jangjeon mathematical society Vol.11 No.2
An n−tuple (a₁, a₂, . . . , an) is symmetric (more pricisely palindromic), if ak = an−k+₁, 1 ≤ k ≤ n. A symmetric n-sigraph is an ordered pair Sn = (G, δ), where G = (V,E) is a graph called the underlying graph of Sn and δ : E → Hn is a function. In this paper, we obtain some results by introducing few notions of balance in symmetric n-sigraphs.
Switching equivalence in symmetric -sigraphs
R. Rangarajan,P. Siva Kota Reddy,M. S. Subramanya 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
An n-tuple (a1, a2, ..., an) is symmetric, if ak = an−k+1, 1 ≤ k≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, б) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and [수식] : E → Hn (μ : V → Hn) is a function. Analogous to the concept of the common-edge sigraph of a sigraph, common-edge symmetric n-sigraph of a symmetric n-sigraph is defined. Further, we obtain some switching equivalent characterizations between common-edge symmetric n-sigraph, line symmetric n-sigraph and jump symmetric n-sigraph.
On three techniques of approximations for Volterra’ population-type model
R. Rangarajan,Nanjundaswamy N. 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.4
In the present paper, series solution by a decomposition technique,Pade approximation technique and asymptotic approximation technique are applied to solve a Volterra’s population-type model which has exact solution not only for non integral part but also for integral part. Like a typical solution of Volterra’s population model, the approximate solution with the range in between 0 and 1, exhibits a population rise along the logistic curve followed by a decay to zero in the long run.
Switching Invariant Neighborhood Signed Graphs
R. Rangarajan,M. S. Subramanya,P. S. K. Reddy 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.2
A signed graph (marked graph) is an ordered pair S = (G, ) (S = (G, μ)),where G = (V,E) is a graph called the underlying graph of S and [수식] is a function. The neighborhood graph of a graph G = (V,E), denoted by N(G),is a graph on the same vertex set V , where two vertices in N(G) are adjacent if, and only if, they have a common neighbor. Analogously, one can define the neighborhood signed graph N(S) of a signed graph [수식] as a signed graph,[수식] where N(G) is the underlying graph of N(S), and for any edge e = uv in N(S),[수식] where for any v 2 V , μ(v) =Y u)μ(v), where for any v 2 V , μ(v) = u2N(v) (uv). In this paper, we characterize signed graphs S for which S N(S), Sc N(S) and N(S) J(S), where J(S) and Sc denotes jump signed graph and complement of signed graph of S respectively.
A pair of classical orthogonal polynomials connected to Catalan numbers
R. Rangarajan,Shashikala P. 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
In the present paper, a pair of classical orthogonal polynomials are extracted from denominator polynomials of even and odd order convergents of a regular C- fraction connected to Pade approximants for the generating function of Catalan numbers. The characteristic features of classical orthogonal polynomials are described with the help of their close connections to Chebyshev polynomials of second and third kind.
Laplace decomposition method for solving certain differential-difference equations both of order 1
Ananth Kumar S. R,R. Rangarajan 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.3
In the present paper, exact or approximate solution of certain differentialdifference equations both of order 1 is presented using Laplace decomposition method. The method is motivated by Laplace decomposition methods for solving differential equations and Integro-differential equations available in the recent literature. The aim of this paper is to workout an efficient iterative procedure which produces exact or approximate solution for the present problem in a simple and elegant fashion. This method transforms a first order differential-difference equation with given initial condition into an algebraic equation suitable for applying inverse Laplace transformation resulting a series expression involving unit step functions, representing the solution. The method is implemented on two interesting illustrative examples.
A New Combined Homotopy-Laplace Decomposition Method for Solving DDEs of Order (1, 2)
Ananth Kumar S. R.,R. Rangarajan 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.1
In the recent literature, nonlinear problems are solved by two powerful decomposition methods, namely, Laplace decomposition method and Homotopy analysis methods. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations of order (1, 2).
THE MINIMUM EQUITABLE DOMINATING COLOR ENERGY OF A GRAPH
P. Rajendran,R. Rangarajan 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.3
The color energy of a graph was introduced by C. Adiga et.al.[2]. Motivated by this work, we introduce a new matrix called the minimum equitable dominating color matrix of a graph. Further we establish the minimum equitable dominating color energy of some standard graphs with their bounds.