‎recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎in this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎then we use this construction to generalize the result due to cook and nagel‎.

The paper describes a method to determine symmetrized weight enumerators of Zpm -linear codes based on the notion of a disjoint weight enumerator. Symmetrized weight enumerators are given for the lifted quadratic residue codes of length 24 modulo 2 and modulo 3 , for any positive m .

The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, date it has only been possible completely characterize HEC for at most $n=5$ parties. For larger $n$, our knowledge falls short incomplete: almost nothing is known about extremal elements. Here, we introduce a symmetrizati...

A completely decomposable group is an abelian group of the form ⊕ i Hi, where Hi ≤ (Q,+). We show that every computable completely decomposable group is ∆5-categorical. We construct a computable completely decomposable group which is not ∆4-categorical, and give an example of a computable completely decomposable group G which is ∆4-categorical but not ∆3-categorical. We also prove that the inde...

The recent discovery that the exponent of matrix multiplication is determined by the rank of the symmetrized matrix multiplication tensor has invigorated interest in better understanding symmetrized matrix multiplication. I present an explicit rank 18 Waring decomposition of $sM_{\langle 3\rangle}$ and describe its symmetry group.

Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).