Given two graphs H 1 and 2 , a graph is ( ) -free if it contains no induced subgraph isomorphic to or . For positive integer t, P t the chordless path on vertices. A paraglider that consists of chorless cycle C 4 plus vertex adjacent three vertices In this paper, we study structure 5 paraglider)-free graphs, show every such G satisfies ? ? ? 3 ? ? where are chromatic number clique G, respective...

Let $D\geq 1$ and $q\geq 3$ be two integers. $H(D)=H(D,q)$ denote the $D$-dimensional Hamming graph over a $q$-element set. ${\mathcal T}(D)$ Terwilliger algebra of $H(D)$. $V(D)$ standard T}(D)$-module. $\omega$ complex scalar. We consider unital associative $\mathfrak K_\omega$ defined by generators relations. The are $A$ $B$. relations $A^2 B-2 ABA +B A^2 =B+\omega A$, $B^2A-2 BAB+AB^2=A+\om...

Representation theory for the Jordanian quantum algebra Uh(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of Uh(sl(2)) on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the gener...

After careful introduction and discussion of the concepts involved, procedures are developed to compute Racah and Clebsch-Gordan coefficients for general r-fold tensor products of the U(N) groups. In the process, the multiplicity of a given irreducible representation (irrep) in the direct sum basis is computed, and generalized Casimir operators are introduced to uniquely label the multiple irre...

Abstract. We show that multivariable colored link invariants are derived from the roots of unity representations of Uq(g). We propose a property of the Clebsch-Gordan coefficients of Uq(g), which is important for defining the invariants of colored links. For Uq(sl2) we explicitly prove the property, and then construct invariants of colored links and colored ribbon graphs, which generalize the m...

The SO(5)⊃ SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1, 1)× SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃ SO(3) spherical harmonics and use them to compute the Clebsc...

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S = { (x, y, z) : x + y + z = 1 } . Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and Clebsch-Gordan coefficients. The findings of the present paper constitute a basis upon which one can build formal procedures fo...