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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 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 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)