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In this paper we establish some upper bounds for the largest of minimum degree eigenvalues and a lower bound for the largest of minimum degree eigenvalues of trees.
In this note we give an upper bound for λ(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 .
In this paper we give two integral representations for the Ramanujan's cubic continued fraction V (q) and also derive a modular equation relating V (q) and V (q 3). We also establish some modular equations and a transformation formula for Ra-manujan's theta-function. As an application of these, we compute several new explicit evaluations of theta-functions… (More)
Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan's forty… (More)
Let λ = (λ1, · · · , λm) be a partition of k. Let r λ (n) denote the number of solutions in integers of λ1x 2 1 + · · · + λmx 2 m = n, and let t λ (n) denote the number of solutions in non negative integers of λ1x1(x1 + 1)/2 + · · · + λmxm(xm + 1)/2 = n. We prove that if 1 ≤ k ≤ 7, then there is a constant c λ , depending only on λ, such that r λ (8n + k) =… (More)
In this paper, we obtain a q-analogue of a double inequality involving the Euler gamma function which was first proved geometrically by Alsina and Tomás  and then analytically by Sándor .
In this paper, we obtain some new transformation formulas for Ramanujan's 1 ψ 1 summation formula and also establish some eta-function identities. We also deduce a q-gamma function identity, an q-integral and some interesting series representations for π 3/2 2 √ 2Γ 2 (3/4) and the beta function B(x, y) .
In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bounds given by Beineke and Hegde  and Adiga, Ramaswamy and Somashekara , for n ≥ 28.