Given a directed graph, there exists a universal operator algebra and universal C-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C-algebra of an operator algebra. We also discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isom...

An active area of research in computational science is the design algorithms for solving subgraph matching problem to find copies a given template graph larger world graph. Prior works have largely addressed single-channel networks using variety approaches. We present suite filtering methods isomorphisms multiplex (with different types edges between nodes and more than one edge within each chan...

Thesis Work on Algebraic Geometry The homogeneous cubic polynomials in four variables x, y, z and w form a 20 dimensional vector space over C. Let S ⊂ P be a surface defined by the equation f(x, y, z, w) = a0x 3 + a1x y + · · ·+ a19w = 0, which naturally determines a point [a0, . . . , a19] ∈ P. X admits a natural G = SL(4;C) action. Let X denote the smooth cubic surfaces, X the semistable ones...

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.