17919993
A Note on the Edge-Connectivity of Cages
A (k; g)-graph is a k-regular graph with girth g. A (k; g)-cage is a (k; g)-graph with the smallest possible number of vertices. In this paper we prove that (k; g)cages are k-edge-connected if k ≥ 3 and g is odd.
6641485
On total covers of graphs
A total cover of a graph G is a subset of V(G)∪E(G) which covers all elements of V(G)∪E(G). The total covering number α2(G) of a graph G is the minimum cardinality of a total cover in G. In [1], it is proven that α2(G)⩽[n2] for a connected graph G of order n. Here we consider the extremal case and give some properties of connected graphs which have a total covering number [n2]. We prove that such a graph with even order has a 1-factor and such a graph with odd order is factor-critical.
19646455
The upper bound of essential cyclomatic numbers of hypergraphs
Abstract The essential cyclomatic number of a hypergraph is the maximum number of independent essential cycles of the hypergraph. In this paper, we first prove a general upper bound for the cyclomatic number in terms of the size, order and edge-size of a hypergraph. Then we give a sharp upper bound for ( n −2)-uniform hypergraphs of order n by solving an extremal problem of graphs. It is remarkable that this sharp upper bound is not generally achieved by the complete ( n −2)-uniform hypergraphs.
31774377
Factors in graphs with odd-cycle property
Abstract We present some conditions for the existence of a ( g , f )-factor or a ( g , f )-parity factor in a graph G with the odd-cycle property that any two odd cycles of G either have a vertex in common or are joined by an edge.
206571042
An Upper Bound for the Independent Domination Number
Let G be a simple graph of order n and minimum degree ?. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. In this paper, we show that i(G)?n+2??2n?. Thus a conjecture of Favaron is settled in the affirmative.
11520313
Linear Vertex Arboricity, Independence Number and Clique Cover Number
The linear vertex-arboricity of a graph G is defined to the minimum number of subsets into which the vertex-set G can be partitioned so that every subset induces a linear forest. In this paper, we give the upper and lower bounds for sum and product of linear vertex-arboricity with independence number and with clique cover number respectively. All of these bounds are sharp.
1667264
Path extendability of claw-free graphs
Let G be a connected, locally connected, claw-free graph of order n and x,y be two vertices of G. In this paper, we prove that if for any 2-cut S of G, S@?{x,y}=@A, then each (x,y)-path of length less than n-1 in G is extendable, that is, for any path P joining x and y of length h(
6624380
Structural Features of Toxic Chemicals for Specific Toxicity
We have studied the structural features of toxic chemicals from the RTECS database associated with specific toxicity. The frameworks, functional groups, and structure patterns of molecules are taken into account. Potential active frameworks, groups, and structure patterns for specific toxicity are gained by computational chemistry approaches. These structural features of toxic chemicals will be helpful in understanding activities of toxic chemicals and useful in predicting the toxicity of chemicals, especially in the early stage of drug design.
11111374
Neural Network Based Stereotyping for User Profiles
This paper discusses an approach of establishing system models of users’ task related characteristics, such as domain knowledge in human-computer interaction. Several neural networks are tested for the modelling process. These networks function as associative memories that capture the causal relationships among assumptions about the users’ characteristics. The outputs from the networks are considered as stereotypes assigned to individual users. It is suggested that this approach can be expected to overcome some limitations of user modelling approaches in terms of pattern recognition and classification.
29234559
Quasi-abelian cayley graphs and parsons graphs
LetGbe a finite group, andSa subset ofGwith 1?SandS-1=S.IfSis a union of conjugacy classes ofG,then the Cayley graphX=Cay(G, S)onGwith respect toSis calledquasi-abelian.In this paper we prove that any connected quasi-abelian Cayley graph is hamiltonian (Theorem 2). As a consequence, we prove that Zaks' three conjectures on Parsons graphs are true, with one exception.
37975436
Complexity-Distortion Optimal Search Algorithm for Block Motion Estimation