Semifinite Harmonic Functions on the Zigzag Graph

on the harmonic index of graph operations

‎the harmonic index of a connected graph $g$‎, ‎denoted by $h(g)$‎, ‎is‎ ‎defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in g‎. ‎in this paper‎, ‎expressions for the harary indices of the‎ ‎join‎, ‎corona product‎, ‎cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.

Some Results on Nonlinear Zigzag Functions

Zigzag functions were deened by Brassard, Cr epeau and SS antha 1] in connection with an application to the construction of oblivious transfers (a useful tool in cryptographic protocols). They proved that linear zigzag functions are equivalent to self-intersecting codes, which have been studied by several researchers. In this paper, we begin an investigation of general (linear or non-linear) zi...

Semifinite Spectral Triples Associated with Graph C-algebras

We review the recent construction of semifinite spectral triples for graph C∗algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state. Alan L. Carey Mathematical Sciences Institute Aust...

More on Harmonic Functions

On Univalent Harmonic Functions

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...