Certain chromatic sums of some cycle-related graph classes

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

Some Classes of Alternating Weighted Binomial Sums

In this paper, we consider three classes of generalized alternating weighted binomial sums of the form n ∑ i=0 ( n i ) (−1) f (n, i, k, t) where f (n, i, k, t) will be chosen as UktiVkn−k(t+2)i, UktiVkn−kti and UtkiV(k+1)tn−(k+2)ti. We use the Binet formula and the Newton binomial formula to prove the claimed results. Further we present some interesting examples of our results.

1978 ] Some Classes of Fibonacci Sums 411

Skew Chromatic Index of Certain Classes of Graphs

A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, skew edge coloring of certain classes of graphs are determined. Furthermore, the skew chromatic index of those graphs is obtained ...

Partial sums of certain classes of analytic functions

In this paper, we introduce the class UTq,s([α1] ;α, β) of analytic functions in the open unit disc U = {z ∈ C : |z| < 1} defined by Dziok-Srivastava operator. The object of the present paper is to determine coefficient estimates and some results concerning the partial sums for functions f(z) belonging to this class.