
A complete bipartite graph with the number of two partitions s and t is denoted by
In this work we construct many new examples of maximal partial line spreads in
Low-Density Parity-Check (LDPC) codes have low linear decoding complexity, which is a kind of good codes with excellent performance. Therefore, LDPC codes have great research value. This article is based on vector space over finite field as a theoretical tool by the inclusive relation of vector subspaces to construct protograph, and then constructs the LDPC codes with larger girth based on protograph by the modified progressive edge growth(M-PEG) algorithm, and utilize the related knowledge, such as Anzahl theorem in vector space, determines the code length, code rate and code word number of the LDPC codes. Moreover, the LDPC codes constructed are compared with the existing codes, and the constructed codes are better than some existing ones.
Let G be a graph and a1,…, as be positive integers. The expression
Let
Let G be an edge-colored connected graph. For vertices u and v of G, a shortest u – v path P in G is a u – u geodesic and P is a proper u – u geodesic if no two adjacent edges in P are colored the same. An edge coloring of a connected graph G is called a proper k-geodesic coloring of G for some positive integer k if for every two nonadjacent vertices u and v of G, there exist at least k internally disjoint proper u – u geodesics in G. The minimum number of the colors required in a proper k-geodesic coloring of G is the strong proper k-connectivity
Suppose
An Italian dominating function (IDF) on a graph G = (V,E) is a function f: V → {0,1,2} satisfying the property that for every vertex
This paper mainly presents a construction of LDPC codes based on symplectic spaces. By two subspaces of type (m, r) to produce a subspace of type (m + 1,r) or (m + 1,r + 1) in
We introduce and study a subring SC of
Randic index and geometric-arithmetic index are two important chemical indices. In this paper, we give the generalized Nordhaus-Gaddum-type inequalities for the two kinds of chemical indices.
Graceful graphs were first studied by Rosa [17]. A graceful labeling
An edge-magic total labeling of a graph
A cograph is a simple graph that does not contain an induced path on 4 vertices. A graph G is
We survey Dudeney’s round table problem which asks for a set of Hamilton cycles in the complete graph that uniformly covers the 2-paths of the graph. The problem was proposed about one hundred years ago but it is still unsettled. We mention the history of the problem, known results, gener-alizations, related designs, and some open problems.
Constructions are given for non-cubic, edge-critical Hamilton laceable bigraphs with 3m edges on 2m vertices for all m ≥ 4. The significance of this result is that it shows the conjectured hard upper bound of 3m edges for edge-critical bigraphs on 2m vertices is populated by both cubic and non-cubic cases for all m. This is unlike the situation for the hard 3m-edge lower bound for edge-stable bigraphs where the bound is populated exclusively by cubics.
In this paper, we identify LOW and OLW graphs, find the minimum
A maximal independent set is an independent set that is not a proper subset of any other independent set. A twinkle graph W is a connected unicyclic graph with cycle C such that W – x is disconnected for any
1970-2025 CP (Manitoba, Canada) unless otherwise stated.