Braided subfactors of von Neumann algebras provide a framework for studying two dimensional conformal field theories and their modular invariants. We review this in the context of SU(3) conformal field theories through corresponding SU(3) braided subfactors and various subfactor invariants including spectral measures for the nimrep graphs, A2-planar algebras and almost Calabi-Yau algebras.

Let Y ′′ be a pseudo-Maxwell–von Neumann prime. Recent developments in quantum calculus [6, 18] have raised the question of whether i′ > ∅. We show that Banach’s conjecture is true in the context of graphs. It would be interesting to apply the techniques of [6] to scalars. In this context, the results of [18] are highly relevant.

The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses Fuglede–Kadison determinants, while another uses effective resistance. We use the latter to prove that tree entropy respects stochastic domination. We also prove th...

1 Cauer, W., "Die Verwirklichung von Wechselstromswiderstanden vorgeschriebener Frequenzabhangigkeit," Arch. f. Elektrotechnik, 17, 355 (1926). 2 McMillan, B., "Introduction to Formal Realizability Theory," Bell Syst. Tech. J., 31, 217 (1952). 8 Mason, S. J., "Signal Flow Graphs," Proc. I.R.E., 39, 297 (1951). 4 Luce, R. D., "Two Decomposition Theorems for a Class of Finite Oriented Graphs," Am...

The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses Fuglede-Kadison determinants, while another uses effective resistance. We use the latter to prove that tree entropy respects stochastic domination. We also prove th...

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.

In 1927, the topologist Karl Menger published an article called Zur allgemeinen Kurventheorie (On the general theory of curves), in which he stated a remarkable result, now one of the most fundamental results in graph theory: Satz. Ist K ein kompakter regull ar eindimensionaler Raum, welcher zwi-schen den beiden endlichen Mengen P und Q n-punktig zusammenhh angend ist, dann enthh alt K n paarwe...