Graph products of groups were introduced by Green in her thesis [32]. They have an operator algebraic counterpart and explored [14]. In this paper we prove Khintchine type inequalities for general C?-algebraic graph which generalize results Ricard Xu [50] on free C?-algebras. We apply these the context (right-angled) Hecke C?-algebras, are deformations group algebra Coxeter (see [22]). For dedu...

Identifying the parallelism in a problem by partitioning its data and tasks among the processors of a parallel computer is a fundamental issue in parallel computing. This problem can be modeled as a graph partitioning problem in which the vertices of a graph are divided into a speciied number of subsets such that few edges join two vertices in diierent subsets. Several new graph partitioning al...

We conjecture a new lower bound on the algebraic connectivity of graph that involves number vertices high eccentricity in graph. prove this implies strengthening Laplacian Spread Conjecture. discuss further conjectures, also Conjecture, include for simple graphs and weighted graphs.

Spectral graph theory discusses about the algebraic properties of graphs based on spectrum a graph. This article investigated prism The method used in this research is circulant matrix. results showed that P2,s regular degree 3, for s odd and ≥ circulantt with spectrum.

A caterpillar unicyclic graph is a unicyclic graph in which the removal of all pendant vertices makes it a cycle. In this paper, the unique caterpillar unicyclic graph with minimum algebraic connectivity among all caterpillar unicyclic graphs is determined.

Repeat-Accumulate (RA) codes, consisting of a simple binary repetition followed by a permutation and an accumulator, are converting into quasi-cyclic codes with multiple cross-linked cycles. The algebraic heuristics are used to design codes with an explicit algebraic permutation yielding desirable graph properties. Recursive graph constructions techniques are given for the construction of very ...

This paper is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best-known as the algebraic connectivity of G, denoted a(G). Emphasis is given on classifications of bounds to algebraic connectivity as a function of other graph invariants, as well as the applications of Fiedler vectors (eigenvectors related to a(G)) on trees, on hard problems in graphs and also on the com...