相关论文: Zig-zag and Replacement Product Graphs and LDPC Co…
A classical t-tensor product expander is a natural way of formalising correlated walks of t particles on a regular expander graph. A quantum t-tensor product expander is a completely positive trace preserving map that is a straightforward…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
A new product construction of graphs and digraphs, based on the standard box product of graphs and called the separated box product, is presented, and several of its properties are discussed. Questions about the symmetries of the product…
Product structure theorems are a collection of recent results that have been used to resolve a number of longstanding open problems on planar graphs and related graph classes. One particularly useful version states that every planar graph…
We investigate the coboundary expansion property of tensor product codes, known as product expansion, which plays an important role in recent constructions of good quantum LDPC codes and classical locally testable codes. Prior research has…
Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. The (weighted) size difference of this bipartition is a lower bound for the…
Generalized Product (GPC) Codes, an unification of Product Codes and Integrated Interleaved (II) Codes, are presented. Applications for approaches requiring local and global parities are described. The more general problem of extending…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum…
Let $d \geq 1$ be an integer. From a set of $d$-dimensional vectors, we obtain a $d$-\dpg\ by letting each vector $\va^u$ correspond to a vertex $u$ and by adding an edge between two vertices $u$ and $v$ if and only if their dot product…
We investigate Cayley graphs of graph products by showing that graph products with vertex groups that have isomorphic Cayley graphs yield isomorphic Cayley graphs.
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Graph product structure theory expresses certain graphs as subgraphs of the strong product of much simpler graphs. In particular, an elegant formulation for the corresponding structural theorems involves the strong product of a path and of…
Product LDPC codes take advantage of LDPC decoding algorithms and the high minimum distance of product codes. We propose to add suitable interleavers to improve the waterfall performance of LDPC decoding. Interleaving also reduces the…
Given a graph $G=(V,E)$, an integer $k$, and a function $f_G:V^k \times V^k \to {0,1}$, the $k^{th}$ graph product of $G$ w.r.t $f_G$ is the graph with vertex set $V^k$, and an edge between two vertices $x=(x_1,...,x_k)$ and…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
Counting short cycles in bipartite graphs is a fundamental problem of interest in the analysis and design of low-density parity-check (LDPC) codes. The vast majority of research in this area is focused on algorithmic techniques. Most…
The wreath product of graphs is a graph composition inspired by the notion of wreath product of groups, with interesting connections with Geometric Group Theory and Probability. This paper is devoted to the description of some degree and…
This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints.…
A graph $\Gamma$ is said to be stable if $\mathrm{Aut}(\Gamma\times K_2)\cong\mathrm{Aut}(\Gamma)\times \mathbb{Z}_{2}$ and unstable otherwise. If an unstable graph is connected, non-bipartite and any two of its distinct vertices have…