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1.
林诒勋 《高校应用数学学报(英文版)》2003,18(3):361-369
§ 1 IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th… 相似文献
2.
Let G = (V,E) be a graph without isolated vertices.A set S V is a domination set of G if every vertex in V - S is adjacent to a vertex in S,that is N[S] = V.The domination number of G,denoted by γ(G),is the minimum cardinality of a domination set of G.A set S C V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching.The paired-domination number,denoted by γpr(G),is defined to be the minimum cardinality of a paired-domination set S in G.A subset S V is a power domination set of G if all vertices of V can be observed recursively by the following rules: (i) all vertices in N[S] are observed initially,and (ii) if an observed vertex u has all neighbors observed except one neighbor v,then v is observed (by u).The power domination number,denoted by γp(G),is the minimum cardinality of a power domination set of G.In this paper,the constructive characterizations for trees with γp = γ and γpr = γp are provided respectively. 相似文献
3.
Let G =(V,E) be a graph without isolated vertices.A set S V is a domination set of G if every vertex in V -S is adjacent to a vertex in S,that is N[S] = V .The domination number of G,denoted by γ(G),is the minimum cardinality of a domination set of G.A set S V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S]has a perfect matching.The paired-domination number,denoted by γpr(G),is defined to be the minimum cardinality of a paired-domination set S in G.A subset S V is a power domination set of G if all vertices of V can be observed recursively by the following rules:(i) all vertices in N[S] are observed initially,and(ii) if an observed vertex u has all neighbors observed except one neighbor v,then v is observed(by u).The power domination number,denoted by γp(G),is the minimum cardinality of a power domination set of G.In this paper,the constructive characterizations for trees with γp = γ and γpr = γp are provided respectively. 相似文献
4.
Let G = (V, E) be a graph without isolated vertices. A set S lohtain in V is a domination set of G if every vertex in V - S is adjacent to a vertex in S, that is N[S] = V. The domination number of G, denoted by γ(G), is the minimum cardinality of a domination set of G. A set S lohtain in V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching. The paired-domination number, denoted by γpr(G), is defined to be the minimum cardinality of a paired-domination set S in G. A subset S lohtain in V is a power domination set of G if all vertices of V can be observed recursively by the following rules: (i) all vertices in N[S] are observed initially, and (ii) if an observed vertex u has all neighbors observed except one neighbor v, then v is observed (by u). The power domination number, denoted by γp(G), is the minimum cardinality of a power domination set of G. In this paper, the constructive characterizations for trees with γp=γ and γpr = γp are provided respectively. 相似文献
5.
σ-多项式的根 总被引:2,自引:0,他引:2
§ 1 IntroductionAll graphs considered are finite and simple.Undefined notation and terminology willconform to those in[1 ] .Let V(G) ,E(G) and Gdenote the vertex set,edge set and complement of a graph G,respectively. Let P(G,x) andσ(G,x) denote the chromatic polynomial andσ-polynomialof G,respectively.The log-concavity property of the chromatic polynomial andσ-polyno-mial of G has a close relation to their roots,which were well studied in[2 ,3] .Results onthe study of the roots of… 相似文献
6.
Let G=(V,E) be a graph.A set S■V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S.The restrained domination number of G,denoted γr(G),is the smallest cardinality of a restrained dominating set of G.In this paper,we show that if G is a graph of order n≥4,then γr(G)γr(G)≤2n.We also characterize the graphs achieving the upper bound. 相似文献
7.
Marcin KRZYWKOWSKI 《数学年刊B辑(英文版)》2012,33(1):113-126
A vertex of a graph is said to dominate itself and all of its neighbors.A double dominating set of a graph G is a set D of vertices of G,such that every vertex of G is dominated by at least two vertices of D.The double domination number of a graph G is the minimum cardinality of a double dominating set of G.For a graph G =(V,E),a subset D V(G) is a 2-dominating set if every vertex of V(G) \ D has at least two neighbors in D,while it is a 2-outer-independent dominating set of G if additionally the set V(G)\D is independent.The 2-outer-independent domination number of G is the minimum cardinality of a 2-outer-independent dominating set of G.This paper characterizes all trees with the double domination number equal to the 2-outer-independent domination number plus one. 相似文献
8.
Let G =(V, E) be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f:V∪E→ {-1, 1} such that ∑_(y∈N_m(x)∪{x})f(y)≥ 1for every element x∈V∪E, where N_m(x) is the set of elements of V∪E adjacent or incident to x. The weight of f is w(f) =∑_(x∈V∪E)f(x). The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs. 相似文献
9.
WANG Tao&YU QingLin Institute of Applied Mathematics College of Mathematics Information Science Henan University Kaifeng China 《中国科学 数学(英文版)》2010,(5)
For a graph G =(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination number γ(G) of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,if γ(G-v) γ(G) for any vertex v in G.A graph G is domination edge critical,if γ(G ∪ e) γ(G) for any edge e ∈/E(G).We call a graph G k-γ-vertex-critical(resp.k-γ-edge-critical) if it is domination vertex critical(resp.domination edge critical) and γ(G) = k.Ananchuen and Plummer posed the conjecture:Let G be a k-connected graph with the minimum degree at least k+1,where k 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is k-factor-critical.In this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph. 相似文献
10.
Eduardo lvarez-Miranda Alfredo Candia-Vjar Xu-jin CHEN Xiao-dong HU Bi LI 《应用数学学报(英文版)》2014,30(1):1-26
Given a connected graph G=(V,E)with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree(PCST)problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c+e]while taking risk(c+e xe)/(c+e c e)of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p+v]for its inclusion in T while taking risk(yv p v)/(p+v p v)of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable. 相似文献
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本文研究的问题是确定e*(p,B)的值,也就是确定顶点数为p、带宽为B的连通图G的最小边数,本文给出当B=p+3/2和B=p/2+2时的精确结果。 相似文献
14.
本文研究的问题是确定f(p,B)的值,也就是给定顶点数p和带宽B,求满足最大度不超过B的连通图的最小边数,本文给出了一些f(p,B)的值及相应极图。 相似文献
15.
决定了4p(p是奇素数)阶二面体群的连通3度Cayley图的完全分类,并证明4p阶二面体群不是弱3-CI群,从而否定了C.H.Li关于"所有有限群都是弱3-CI群"的猜想 相似文献
16.
《数学季刊》2016,(2):111-117
Let D(G) = (dij )n×n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vj in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a su?cient and necessary condition for complete r-partite graphs Kp1,p2,··· ,pr =Ka1·p1,a2·p2,··· ,as···ps to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs Ka1·p1,a2·p2,··· ,as·ps with s>4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs Ka1·p1,a2·p2,··· ,as·ps with s = 5, 6. The problem of the existence of such distance integral graphs Ka1·p1,a2·p2,··· ,as·ps with arbitrarily large number s remains open. 相似文献
17.
The conditional independence structure of a common probability measure is a structural model. In this paper, we solve an open problem posed by Studeny [Probabilistic Conditional Independence Structures, Theme 9, p. 206]. A new approach is proposed to decompose a directed acyclic graph and its optimal properties are studied. We interpret this approach from the perspective of the decomposition of the corresponding conditional independence model and provide an algorithm for identifying the maximal prime subgraphs in a directed acyclic graph. 相似文献
18.
关于图的L(2,1)标号核图 总被引:3,自引:0,他引:3
图的L(2,1)标号核图来自频率分配问题而导致的图论问题.在本文中,我们证得(i)对任意简单图G,存在G的一个标号核图Gcore,使得L(G)=L(Gcore)和L(G)≥|V(Gcore)|-1;(ii)设图G有p个顶点且边集|E(G)|≠φ,存在路
Pi G(1≤i≤m)和路Hs G(1≤s≤n),其中在G中V(Pi)∩V(Pj)=φ(i≠j),在G中V(P,)∩V(Pt)=φ(s≠t),则有m∑t=1|V(Pt)|+n∑s=1|V(Hs)|-(m+n)≥p;(iii)G是p(p≥5)个顶点的简单图,则有p+3≤L(G)+L(G)≤3p-4. 相似文献
19.
李学文 《数学的实践与认识》2005,35(8):233-238
群G关于S的有向Cayley图X=Cay(G,S)称为pk阶有向循环图,若G是pk阶循环群.利用有限群论和图论的较深刻的结果,对p2阶弧传递(有向)循环图的正规性条件进行了讨论,证明了任一p2阶弧传递(有向)循环图是正规的当且仅当(|Aut(G,S)|,p)=1. 相似文献