Chandrashekara Adiga

Bounds on the Distance Energy and the Distance Estrada Index of Strongly Quotient Graphs

The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada index of CSQG whose diameter does not exceed two. Additionally, we show that our results improve most of the results obtained by Gungor and Bozkurt (2009) and Zaferani (2008).

A note on strongly multiplicative graphs

In this note we give an upper bound for ∏(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bound obtained by Beineke and Hegde [1]. Keywords and phrases:graph labeling, strongly multiplicative graphs.

A basic bilateral series summation formula and its applications

We obtain an interesting 2ψ2 summation formula and demonstrate its diverse uses leading to some (i) sums of squares theorems (ii) Ramanujans Fourier series developments related to theta-functions (iii) Lambert series identities related to Dedekind eta-function (iv) q-gamma and g-beta identities.

On some generalizations of Ramanujan’s continued fraction identities

In this note we establish continued fraction developments for the ratios of the basic hypergeometric function2ϕ1(a,b;c;x) with several of its contiguous functions. We thus generalize and give a unified approach to establishing several continued fraction identities including those of Srinivasa Ramanujan.

A note on a continued fraction of Ramanujan

Ramanujan recorded many beautiful continued fractions in his notebooks. In this paper, we derive several identities involving the Ramanujan continued fraction c(q), including relations between c(q) and c(q(n)). We also obtain explicit evaluations of c(e(-pirootn)) for various positive integers n.

Ramanujan's remarkable summation formula and an interesting convolution identity

In this note we obtain a convolution identity for the coefficients B(n)(alpha, theta, q) defined by PI(n=1)infinity (1 + 2xq(n) costheta + x2q2n)/PI(n=1)infinity (1 + 2alphaxq(n) costheta + alpha2x2q2n) = SIGMA(n=-infinity)infinity B(n)(alpha, theta, q)x(n) using Ramanujans 1PSI1 summation. The identity contains as special cases convolution identities of Kung-Wei Yang and a few more interesting analogue.

Color Energy Of A Unitary Cayley Graph

Abstract Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xn)c and some gcd-graphs.

A Note on Four-Variable Reciprocity Theorem

We give new proof of a four-variable reciprocity theorem using Heines transformation, Watsons transformation, and Ramanujans 1𝜓1-summation formula. We also obtain a generalization of Jacobis triple product identity.

An estimate of Ramanujan related to the greatest integer function

If a and n are positive integers and if [ ] is the greatest integer function we obtain upper and lower estimates for [GRAPHICS] stated by Ramanujan in his notebooks.

On Ramanujan's general theta function and a generalization of the Borweins' cubic theta functions

The Borwein brothers have introduced and studied three cubic theta functions. Many generalizations of these functions have been studied as well. In this paper, we introduce a new generalization of these functions and establish general formulas that are connecting our functions and Ramanujans general theta function. Many identities found in the literature follow as a special case of our identities. We further derive general formulas for certain products of theta functions.