有向线图中的(k,l)-核

1 Introduction We consider the finite digraphs that do not havemultiple arcs or loops , but pairs of opposite arcs areallowed.LetD=(V,A) be a digraph , whereVisthe set of vertices andAis the set of arcs .If there isan arc (x,y) fromxtoy,thenthe vertexxis …     

Twin domination in generalized Kautz digraphs

Let G = （V,A） be a digraph.A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V ／ T.There exist u,w ∈ T （possibly u = w） such that （u,v）,（v,w） ∈ A.The twin domination number γ＊（G） of G is the cardinality of a minimum twin dominating set of G.In this paper we consider the twin domination number in generalized Kautz digraphs GK（n,d）.In these digraphs,we establish bounds on the twin domination number and give a sufficient condition for the twin domination number attaining the lower bound.We give the exact values of the twin domination numbers by constructing minimum twin dominating sets for some special generalized Kautz digraphs.     

块图中的团横贯集和团独立集

图的一个极大完全子图称为图的一个团．若图G的每一个块为图G的一个团,则称图G为块图．求图的一个最小团横贯集问题和最大团独立集问题分别称为MCTS问题和MCIS问题．文中给出了块图中求解最小团横贯集和最大团独立集的一个线性时间算法,并证明了块图G中的团横贯数等于团独立数,即τc（G）=αc（G）．     

基于油耗和低碳的垃圾收集路径优化研究

随着我国城市垃圾产量的日渐增多,如何使垃圾收运过程无害化、节能化,已成为综合治理环境的新挑战.垃圾收运费用在整个垃圾处理系统中占很大比例,同时随着人们生活水平的提高,人们对生活环境和身体健康更加关注.因此,本文将油耗和碳排放因素考虑到垃圾收集问题中,建立了以运输距离、油耗和碳排放相结合的多目标垃圾收集问题模型,并采用基于插入算法的文化基因算法进行求解,通过标准算例说明了该算法的有效性和实用性.     

几乎正则图的全符号控制

1IntroductionFor notation and graph theory terminology we ingeneral follow[1].LetG=(V,E)be a graph with thevertex setVand the edge setE,andletvbe a vertexinV.The open neighborhood ofvisN(v)={u∈V|uv∈E}and the closed neighborhood ofvisN[v]={v}∪N(v).The d…     

Minus total κ-subdomination in graphs

Let G=(V, E)be a simple graph without isolated vertices. For positive integer κ, a 3-valued function f:V → {-1, 0, 1} is said to be a minus total k-subdominating function(MTκSF)if ∑u∈N(u)f(u)≥ 1 for at least κ vertices v in G, where N(v)is the open neighborhood of v. The minus total κ-subdomination number γ-κt(G)equals the minimum weight of an MTkSF on G. In this paper, the values on the minus total κ-subdomination number of some special graphs are investigated. Several lower bounds on γ-κt of general graphs and trees are obtained.     

图的符号全划分数

Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.     

Bounds on the absorbant number of generalized Kautz digraphs

The generalized Kautz digraphs have many good properties as interconnection network topologies. In this note, the bounds of the absorbant number for the generalized Kautz digraph are given, and some sufficient conditions for the absorbant number of the generalized Kautz digraph attaining the bounds are presented.     

图的整数值控制函数

For an arbitrary subset P of the reals,a function f:V→P is defined to be a P-dominating function of a graph G=(V,E) if the sum of its function values over any closed neighbourhood is at least 1.That is,for every v∈V, f(N[v])≥1.The definition of total P-dominating function is obtained by simply changing‘closed’neighborhood N[v]in the definition of P-dominating function to‘open’neighborhood N(v).The (total) P-domination number of a graph G is defined to be the infimum of weight w(f) =∑_(v∈V)f(v) taken over all (total) P-dominating function f.Similarly,the P-edge and P-star dominating functions can be defined.In this paper we survey some recent progress oil the topic of dominating functions in graph theory.Especially,we are interested in P-,P-edge and P-star dominating functions of graphs with integer values.     

图的整数值控制函数

For an arbitrary subset P of the reals, a function f ： V →P is defined to be a P-dominating function of a graph G = （V, E） if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ∈ V, f（N[v]） ≥ 1. The definition of total P-dominating function is obtained by simply changing ‘closed＇ neighborhood N[v] in the definition of P-dominating function to ‘open＇ neighborhood N（v）. The （total） P-domination number of a graph G is defined to be the infimum of weight w（f） = ∑v ∈ V f（v） taken over all （total） P-dominating function f. Similarly, the P-edge and P-star dominating functions can be defined. In this paper we survey some recent progress on the topic of dominating functions in graph theory. Especially, we are interested in P-, P-edge and P-star dominating functions of graphs with integer values.