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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.
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.
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.
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.
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.
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.
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.
Ranganathan Jaya,Rangarajan Sundaresan Mohan Kumar,Ramasamy Srinivasan 대한영상치의학회 2013 Imaging Science in Dentistry Vol.43 No.3
It has been a challenge to establish the accurate diagnosis of developmental tooth anomalies based on periapical radiographs. Recently, three-dimensional imaging by cone beam computed tomography has provided useful information to investigate the complex anatomy of and establish the proper management for tooth anomalies. The most severe variant of dens invaginatus, known as dilated odontome, is a rare occurrence, and the cone beam computed tomographic findings of this anomaly have never been reported for an erupted permanent maxillary central incisor. The occurrence of talon cusp occurring along with dens invaginatus is also unusual. The aim of this report was to show the importance of cone beam computed tomography in contributing to the accurate diagnosis and evaluation of the complex anatomy of this rare anomaly.
Analysis of Best Channel Feedback and Its Adaptive Algorithms for Multicarrier Wireless Data Systems
Young-June Choi,Rangarajan, S. IEEE 2011 IEEE transactions on mobile computing Vol.10 No.8
<P>Multiuser diversity techniques are used in multicarrier data systems to enhance downlink cell throughput. This requires downlink channel information from the users that is opportunistically used by a base station to send data to the users with good channel condition. Channel feedback from the user to the base station incurs high overhead especially when many users are in the cell and each user needs to report channel information over multiple channels, as in OFDMA systems. To reduce the quantity of feedback information without significant throughput degradation, a practical strategy is to deliver feedback on a partial set of channels with the best channel quality. We call it best feedback, and this reporting scheme carried out for best four or five among 24 channels has been already adopted in the IEEE 802.16e standard. Considering real feedback conditions, we investigate the performance of a best feedback scheme and derive the optimal number of channels for which information needs to be fed back to keep the throughput gap (compared to a full feedback scheme) within a target margin. From the optimal condition, we propose an adaptive best feedback algorithm, where the number of reported channels is adjusted to adapt to the number of users in the cell. We also propose an adjusted periodic feedback algorithm, where users are divided into groups and scheduling is carried out group by group, so a user can report feedback information when his group is scheduled, thereby reducing the frequency of feedback transmission. To support differentiated performance, we further propose heterogeneous feedback algorithms where users are divided into heterogeneous groups, each with a different group size or a different feedback period. Numerical results validate our analysis and provide meaningful insights into the design of various channel feedback schemes.</P>