The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with ( n+1 2 ) edges admits an edge decomposition G = H1 ⊕ · · · ⊕Hn such that Hi has i edges and is isomorphic to a subgraph of Hi+1, i = 1, . . . , n−1. We show that every bipartite graph G with ( n+1 2 ) edges such that the degree sequence d1, . . . , dk of one of the stable sets satisfies di ≥ n − i + 2, 1 ≤ i ...

We describe the twisted affine superalgebra sl(2|2)(2) and its quantized version Uq[sl(2|2)]. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra Uq[osp(2|2)]. We work out the tensor product decomposition explicitly and find the decomposition is not completely reducible. Associated with this 4-dimensional grade star...

A new decomposition for square matrices is constructed by using two known matrix decompositions. characterization of the core-EP order obtained this decomposition. We also use to investigate minus, star, sharp and core partial orders in setting complex matrices.

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, this new notion called homogeneous modules not only captures the classical graph modules but also allows to handle 2−connected components, star-cutsets, and ot...

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, the terminology " module " not only captures the classical graph modules but also allows to handle 2−connected components, star-cutsets, and other vertex subse...

A new star pattern recognition method is developed using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding cataloged vector matrix in a reference frame. It is shown that singular values and right singular vectors are invariant with respect to coordinate transformation and robust under uncertainty. One advantage of singular value co...

A decomposition of a graph is set subgraphs whose edges partition those $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic can be decomposed into spanning tree, 2-regular subgraph, and matching. It has been settled for special classes graphs, one the first results being Hamiltonian graphs. In past two years several new have obtained, adding ...

Some problems related to security in communication networks lead to consider a new type of connectivity in graphs, namely the confidential connectivity. In this paper we present a characterization of unbreakable graphs using the notion of weak decomposition and we give some applications of minimal unbreakable graphs. In fact, we showed that a graph G is confidentially connected if and only if i...