Colored energy of a graph

Chandrashekar Adiga,E. Sampathkumar,M. A. Sriraj,Shrikanth A S 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.3

In this paper, we introduce the concept of color energy of a graph, Ec(G) andcompute the color energy Ex(G) of few families of graphs with minimum number ofcolors. It depends on the underlying graph and colors on its vertices. We establishan upper bound and a lower bound for color energy. Also we introduce the conceptof complement of a colored graph and compute energies of complement of coloredgraphs of few families of graphs.

Nature of a Firm, Degree of Cluster Linkages, and Innovation: A Study of Bengaluru High-tech Manufacturing Cluster

Chandrashekar, Deepak Asian Society for Innovation and Policy 2018 Asian Journal of Innovation and Policy Vol.7 No.1

It is generally understood that clusters are the promoters of innovation and therefore, the attention of researchers has been increasingly to discern the factors driving innovation among the firms in a cluster, especially in a high-tech cluster. In this study, we identify the variables capturing the nature of a firm that possibly impact the absorptive capacity of a firm and subsequently ascertain their impact on the degree of interactions between a firm, and other firms and associated institutions within and outside a cluster, respectively. Furthermore, we probe the influence of these interactions as a whole on firm-level innovation. The study was carried out in the context of Bengaluru, which houses the densely interconnected network of innovation-intensive high-tech manufacturing firms forming a high-tech manufacturing cluster. Data were drawn from 101 high-tech manufacturing firms belonging to electronics, machine tools, electrical and pharmaceutical industries. Based on the cluster analysis and subsequent graphical analysis on each of the three profiled clusters, it was found that size and origin of a firm have significant impact on the degree of firm's interactions. In turn, higher dynamism of firms in terms of degree of interactions led to higher innovation performance.

Arithmetic properties of partition four tuples with 3-cores

Chandrashekar Adiga,Ranganatha D 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.3

Let A<sup>k<sub>3 (n) denote the number of partition k-tuples of n where each partition is 3- core. In this paper, employing elementary generating function dissection techniques, we establish several innite families of congruences for A<sup>4<sub>3 (n). For example, we proved that for all integers α ≥ 0, k ≥ 0 and n ≥ 0, A<sup>4<sub>3(4<sup>(k+1)n + 5.2<sup>(2k+1) - 4/ 3)≡ 0 mod (4<sup>4k+5 -4)/63), A<sup>4<sub>3(16<sup(k+1)α n + 4<sup>(2k+2)α+1 -4) / 3 ≡ A<sup>4<sub>3(n) mod (64<sup>k+1 -1/63).

Fibonacci Graph and its Energies

Chandrashekar Adiga,Anitha N.,Savitha H. C. 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1

The energy of a graph is dened as the sum of absolute values of its eigenvalues. In this paper, we compute the spectrum and energy of the Fibonacci graph. Numerous matrices can be associated with a graph and their spectrums provide useful information about the graph. In recent times, various other graph energies are studied, based on eigenvalues of several graph matrices. In the present paper, we also establish relationship between the usual energy of the Fibonacci graph and other energies like Signless Lapalcian energy, Randic energy, maximum degree energy, common-neighborhood energy, 2-distance energy and Seidal energy.

Spectra of F-sum graphs and F-product graphs

Chandrashekar Adiga,Rakshith B. R. 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.2

Several graph operations based on subdivision graph and its variants have been introduced by many researchers and their spectral properties have been studied. The F-sum graphs and F-product graphs are one among these graph operations. In literature, many topological indices of F-sum graphs and F-product graphs have been examined. In this paper, we rst introduce two matrix forms named as F-sum matrix and F-product matrix and describe their spectra, and then using the spectra of these matrices, we compute the spectra of F-sum graphs and F-product graphs.

Phytochemical Studies of Phyllanthus debilis

K.S.Chandrashekar,D.Satyanarayana,A.B.Joshi,E.V.S.Subrahmanyam 한국생약학회 2004 Natural Product Sciences Vol.10 No.3

Two Lignans Phyllanthin and Hypophyllanthin, and a steroid b-sitosterol has been isolated from the leaves of Phyllanthus debilis and their structures were established by spectral analysis and direct comparison with authentic samples. This is the first report of occurrence of these compound from P.debilis.

Principal Component Analysis of BGP Update Streams

Xu, Kuai,Chandrashekar, Jaideep,Zhang, Zhi-Li The Korea Institute of Information and Commucation 2010 Journal of communications and networks Vol.12 No.2

In this paper, we propose a novel methodology to identify border gateway protocol (BGP) updates associated with major events - affecting network reachability to multiple ASes - and separate them (statistically) from those attributable to minor events, which individually generate few updates, but collectively form the persistent background noise observed at BGP vantage points. Our methodology is based on principal component analysis, which enables us to transform and reduce the BGP updates into different AS clusters that are likely affected by distinct major events. We demonstrate the accuracy and effectiveness of our methodology through simulations and real BGP data.

Damping BGP Route Flaps

Duan, Zhenhai,Chandrashekar, Jaideep,Krasky, Jeffrey,Xu, Kuai,Zhang, Zhi-Li The Korea Institute of Information and Commucation 2007 Journal of communications and networks Vol.9 No.4

BGP route flap damping(RFD) was anecdotally considered to be a key contributor to the stability of the global Internet inter-domain routing system. However, it was recently shown that RFD can incorrectly suppress for substantially long periods of time relatively stable routes, i.e., routes that only fail occasionally. This phenomenon can be attributed to the complex interaction between BGP path exploration and how the RFD algorithm identifies route flaps. In this paper we identify a distinct characteristic of BGP path exploration following a single network event such as a link or router failure. Based on this characteristic, we distinguish BGP route updates during BGP path exploration from route flaps and propose a novel BGP route flap damping algorithm, RFD+. RFD+ has a number of attractive properties in improving Internet routing stability. In particular, it can correctly suppress persistent route flaps without affecting routes that only fail occasionally. In addition to presenting the new algorithm and analyzing its properties, we also perform simulation studies to illustrate the performance of the algorithm.

IPO/M&A Exits by Venture Capital in India: Do Agency Risks Matter?

Joshi, Kshitija,Chandrashekar, Deepak Asian Society for Innovation and Policy 2018 Asian Journal of Innovation and Policy Vol.7 No.3

Venture Capital Firms (VCs) encounter severe information asymmetry risks at almost every stage in their investment lifecycle. This paper explores the agency risks arising from information asymmetry during the stage of exits by VCs from the funded companies in their portfolio and how that impacts the incidence of specific types of type of exits (IPOs/M&As). In this empirical study, by using the data on IPO and M&A exits from venture capital-funded companies, we show how the ability of prospective buyers to better resolve agency risks is directly correlated with the incidence of the above exit types. Using the technique of logistic regression, we demonstrate that factors such as syndication, specialization focus of the VC firm (in terms of stage and sector) and the level of its social capital (proxied by its age and experience) drive the success rate of exits. This is one of first studies in context of exits from VC funded companies in the Indian context.

Mental health in postgraduate social work curriculum: Review of training contents in Indian schools of social work

Bino Thomas,Pattanashetty Chandrashekar Pradeepkumar 한국사회복지학회 2018 Asian Social Work and Policy Review Vol.12 No.2

Training of social workers according to the changing needs of the society is important. To this end, we decided to review the adequacy of mental health training in postgraduate programme in social work. The Mental Health Care Act 2017 defines psychiatric social worker (PSW) in India to have additional higher qualification beyond post-graduation in social work. The number of such qualified PSWs appears to be limited due to small number of institutes that offer advanced training in the country. Though, the number of available PSWs with such qualifications is rising, the manpower in proportion to the mental health needs in the country continues to remain low. It is therefore, relevant to review the quality of psychiatric social work education at postgraduate level if this level is to be considered as the desirable qualification for PSW. In this context, postgraduate social work syllabi from 71 universities including autonomous institutions were reviewed using semi-structured assessment. The results show a lack of uniform teaching components, training methods and insufficient skill orientation towards mental health interventions. These observations suggest that curricula and training are modified with strengthening and enhancing the quality of training of mental health at post-graduate level in Social Work.