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 establish some upper bounds for the largest of minimum degree eigenvalues and a lower bound for the largest of minimum degree eigenvalues of trees.
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)
In this paper we obtain a q-analogue of J. Sándor's theorems , on employing the q-analogue of Stirling's formula established by D. S. Moak .
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) .
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.  have introduced the concept of color energy of a graph E c (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… (More)
A graph G is said to be Smarandachely harmonic graph with property P if its vertices can be labeled 1, 2, · · · , n such that the function fP : A → Q defined by fp(H) = v∈V (H) f (v) v∈V (H) f (v) , H ∈ A is injective. Particularly, if A is the collection of all paths of length 1 in G (That is, A = E(G)), then a Smarandachely harmonic graph is called… (More)