2737366
A proof of an inequality concerning k-restricted edge connectivity
An edge subset S of a connected graph G is a k-restricted edge cut if G-S is disconnected, and every component of G-S has at least k vertices. The k-restricted edge connectivity is the cardinality of a minimum k-restricted edge cut. In this note, we show that except for a well-defined class of graphs, k-restricted edge cuts of a connected graph G exist for any k=<@d(G)+1, where @d(G) is the minimum degree of G. Furthermore, we obtain an upper bound for k-restricted edge connectivity.
16327244
Semi-hyper-connected edge transitive graphs
A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characterize semi-hyper-connected edge transitive graphs.
32852823
Restricted Edge Connectivity of Edge Transitive Graphs
5888722
The transformation graph Gxyz when xyz=-++
The transformation graph G^-^+^+ of G is the graph with vertex set V(G)@?E(G) in which the vertex x and y are joined by an edge if one of the following conditions holds: (i) x,y@?V(G), and x and y are not adjacent in G, (ii) x,y@?E(G), and x and y are adjacent in G, (iii) one of x and y is in V(G) and the other is in E(G), and they are incident in G. In this paper, it is shown that for two graphs G and G^', G^-^+^+@?G^'^-^+^+ if and only if G@?G^'. Simple necessary and sufficient conditions are given for G^-^+^+ to be planar and hamiltonian, respectively. It is also shown that for a graph G, the edge-connectivity of G^-^+^+ is equal to its minimum degree. Two related conjectures and some research problems are presented.
36772515
On the construction of systematic tEC/AUED codes
A new approach for the construction of systematic tEC/AUED codes is presented. These new constructions improve many values of the upper bound on the redundancy of the code for t=1 and 2. >
6152130
Estimation via compressed information
Some results from classical estimation theory are extended to the case in which data must be communicated from several places where observations are made to the place where the estimate is generated. Particular emphasis is placed on determining how the variance of an unbiased estimator depends on the communication rates. Explicit result are given for Gaussian sources. >
38207892
On the Relations Between Arboricity and Independent Number Or Covering Number
In this paper, the following results are obtained: a(G) + β(G) ⩽ p + 1, ⌈p2⌉ ⩽ a(G)β(G), ⌈p2⌉ ⩽ a′(G) + gb′(G) ⩽ pa′(G) + α′(G) ⩽ 2⌈p2⌉ (δ ⩽ 1) and all bounds are sharp, where p = ¦V(G)¦, ⌈x⌉ denotes the smallest integer greater than or equal to x, a(G) is the vertex arboricity, a′(G) is the edge arboricity, α′(G) is the edge covering number, β(G) is the vertex independent number, β′(G) is the edge independent number, and δ is the minimum degree of G.
6709890
An agent-based hybrid framework for database mining
While knowledge discovery in databases (KDD) is defined as an iterative sequence of the following steps: data pre-processing, data mining, and post data mining, a significant amount of research in data mining has been done, resulting in a variety of algorithms and techniques for each step. However, a single data-mining technique has not been proven appropriate for every domain and data set. Instead, several techniques may need to be integrated into hybrid systems and used cooperatively during a particular data-mining operation. That is, hybrid solutions are crucial for the success of data mining. This paper presents a hybrid framework for identifying patterns from databases or multi-databases. The framework integrates these techniques for mining tasks from an agent point of view. Based on the experiments conducted, putting different KDD techniques together into the agent-based architecture enables them to be used cooperatively when needed. The proposed framework provides a highly flexible and robust data-mining platform and the resulting systems demonstrate emergent behaviors although it does not improve the performance of individual KDD techniques.
37643061
Adjacent strong edge coloring of graphs
Abstract For a graph G ( V , E ), if a proper k -edge coloring ƒ is satisfied with C ( u ) ≠ C ( v ) for uv ∈ E ( G ), where C(u) = {ƒ(uv) | uv ∈ E} , then ƒ is called k-adjacent strong edge coloring of G , is abbreviated k-ASEC , and χ ′ as ( G ) = min { k | k - ASEC of G } is called the adjacent strong edge chromatic number of G . In this paper, we discuss some properties of χ′ as ( G ), and obtain the χ′ as ( G ) of some special graphs and present a conjecture: if G are graphs whose order of each component is at least six, then χ ′ as ( G ) ≤ Δ ( G ) + 2, where Δ( G ) is the maximum degree of G .