共查询到17条相似文献,搜索用时 352 毫秒
1.
Let G be a simple graph. We first show that ■, where δiand di denote the i-th signless Laplacian eigenvalue and the i-th degree of vertex in G, respectively.Suppose G is a simple and connected graph, then some inequalities on the distance signless Laplacian eigenvalues are obtained by deleting some vertices and some edges from G. In addition, for the distance signless Laplacian spectral radius ρQ(G), we determine the extremal graphs with the minimum ρQ(G) among the trees with given diameter, the unicyclic and bicyclic graphs with given girth, respectively. 相似文献
2.
A connected graph G=(V,E) is called a quasi-tree graph if there exists a vertex v_0∈V(G) such that G-v_0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian eigenvalue greater than or equal to n-3.As an application,we determine all quasi-tree graphs of order n with the sum of the two largest signless Laplacian eigenvalues greater than to 2 n-5/4. 相似文献
3.
A tricyclic graph G =(V(G), E(G)) is a connected and simple graph such that|E(G)| = |V(G)|+2. Let Tg nbe the set of all tricyclic graphs on n vertices with girth g. In this paper, we will show that there exists the unique graph which has the largest signless Laplacian spectral radius among all tricyclic graphs with girth g containing exactly three(resp., four)cycles. And at the same time, we also give an upper bound of the signless Laplacian spectral radius and the extremal graph having the largest signless Laplacian spectral radius in Tg n,where g is even. 相似文献
4.
A connected graph G =(V, E) is called a quasi-tree graph, if there exists a vertex v_0 ∈ V(G) such that G-v_0 is a tree. Liu and Lu [Linear Algebra Appl. 428(2008) 2708-2714] determined the maximal spectral radius together with the corresponding graph among all quasi-tree graphs on n vertices. In this paper, we extend their result, and determine the second to the fifth largest spectral radii together with the corresponding graphs among all quasi-tree graphs on n vertices. 相似文献
5.
The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to llth largest signless Laplacian spectral radii in the class of bicyclic graphs with n vertices. Moreover, the unique bicyclic graph with the largest or the second largest signless Laplacian spread among the class of connected bicyclic graphs of order n is determined, respectively. 相似文献
6.
For any vertex u∈V(G), let T_N(U)={u}∪{uv|uv∈E(G), v∈v(G)}∪{v∈v(G)|uv∈E(G)}and let f be a total k-coloring of G. The total-color neighbor of a vertex u of G is the color set C_f(u)={f(x)|x∈TN(U)}. For any two adjacent vertices x and y of V(G)such that C_f(x)≠C_f(y), we refer to f as a k-avsdt-coloring of G("avsdt"is the abbreviation of"adjacent-vertex-strongly- distinguishing total"). The avsdt-coloring number of G, denoted by X_(ast)(G), is the minimal number of colors required for a avsdt-coloring of G. In this paper, the avsdt-coloring numbers on some familiar graphs are studied, such as paths, cycles, complete graphs, complete bipartite graphs and so on. We proveΔ(G) 1≤X_(ast)(G)≤Δ(G) 2 for any tree or unique cycle graph G. 相似文献
7.
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
8.
A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u, v ∈ V (G) there is a vertex w ∈ W such that d(u, w) ≠ d(v, w). A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G, denoted by dim(G). For a vertex u of G and a subset S of V (G), the distance between u and S is the number min s∈S d(u, s). A k-partition Π = {S 1 , S 2 , . . . , S k } of V (G) is called a resolving partition if for every two distinct vertices u, v ∈ V (G) there is a set S i in Π such that d(u, Si )≠ d(v, Si ). The minimum k for which there is a resolving k-partition of V (G) is called the partition dimension of G, denoted by pd(G). The circulant graph is a graph with vertex set Zn , an additive group of integers modulo n, and two vertices labeled i and j adjacent if and only if i-j (mod n) ∈ C , where CZn has the property that C =-C and 0 ■ C. The circulant graph is denoted by Xn, Δ where Δ = |C|. In this paper, we study the metric dimension of a family of circulant graphs Xn, 3 with connection set C = {1, n/2 , n-1} and prove that dim(Xn, 3 ) is independent of choice of n by showing that dim(Xn, 3 ) ={3 for all n ≡ 0 (mod 4), 4 for all n ≡ 2 (mod 4). We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C = {±1, ±2} and prove that pd(Xn, 4 ) is independent of choice of n and show that pd(X5,4 ) = 5 and pd(Xn,4 ) ={3 for all odd n ≥ 9, 4 for all even n ≥ 6 and n = 7. 相似文献
9.
Let G = (V, E) be a primitive digraph. The vertex exponent of G at a vertex v ∈ V, denoted by expG(v), is the least integer p such that there is a v → u walk of length p for each u ∈ V. We choose to order the vertices of G in the k-point exponent of G and is denoted by expG(k), 1 ≤ k ≤ n. We define the k-point exponent set E(n, k) := {expG(k)| G = G(A) with A ∈ CSP(n)}, where CSP(n) is the set of all n × n central symmetric primitive matrices and G(A) is the associated graph of the matrix A. In this paper, we describe E(n,k) for all n, k with 1 ≤ k ≤ n except n ≡ 1(mod 2) and 1 ≤ k ≤ n - 4. We also characterize the extremal graphs when k = 1. 相似文献
10.
An L(3,2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all non-negative integers(labels) such that |f(u)-f(v)|≥3 if d(u,v)=1,|f(u)-f(v)≥2 if d(u,v)=2 and |f(u)-f(v)|≥1 if d(u,v)=3.For a non-negative integer k,a k-L(3,2,1)-labeling is an L(3,2,1)-labeling such that no label is greater than k.The L(3,2,1)-labeling number of G,denoted by λ_(3,2,1)(G), is the smallest number k such that G has a k-L(3,2,1)-labeling.In this article,we characterize the L(3,2,1)-labeling numbers of trees with diameter at most 6. 相似文献
11.
连通图$G$的距离无符号拉普拉斯矩阵定义为$\mathcal{Q}(G)=Tr(G)+D(G)$, 其中$Tr(G)$和$D(G)$分别为连通图$G$的点传输矩阵和距离矩阵. 图$G$的距离无符号拉普拉斯矩阵的最大特征值称为$G$的距离无符号拉普拉斯谱半径. 本文确定了给定点数的双圈图中具有最大的距离无符号拉普拉斯谱半径的图. 相似文献
12.
The Q-index of a graph G is the largest eigenvalue q(G) of its signless Laplacian matrix Q(G). In this paper, we prove that the wheel graph W_n = K_1 ∨C_(n-1)is the unique graph with maximal Q-index among all Halin graphs of order n. Also we obtain the unique graph with second maximal Q-index among all Halin graphs of order n. 相似文献
13.
Yanbin Jia & Changqing Xu 《数学研究通讯:英文版》2009,25(5):429-432
Let $G$ be a multigraph with vertex set $V(G)$. Assume that a positive
integer $f(v$) with $1 ≤ f(v) ≤ d(v)$ is associated with each vertex $v ∈ V$. An edge
coloring of $G$ is called an $f$-edge cover-coloring, if each color appears at each vertex $v$ at least $f(v)$ times. Let $χ′_{fc}(G)$ be the maximum positive integer $k$ for which an $f$-edge cover-coloring with $k$ colors of $G$ exists. In this paper, we give a new lower
bound of $χ′_{fc}(G)$, which is sharp. 相似文献
14.
设$\overrightarrow{G}$ 是一个强连通双圈有向图, $A(\overrightarrow{G})$是其邻接矩阵.设$D(\overrightarrow{G})$ 是$\overrightarrow{G}$的顶点出度的对角矩阵, $Q(\overrightarrow{G})=D(\overrightarrow{G})+A(\overrightarrow{G})$是$\overrightarrow{G}$ 的无符号拉普拉斯矩阵. $Q(\overrightarrow{G})$的谱半径称为$\overrightarrow{G}$的无符号拉普拉斯谱半径.在这篇文章中, 确定了在所有强连通双圈有向图中达到最大或最小无符号拉普拉斯谱半径的唯一有向图. 此外,还证明了任意一个强连通双圈有向图是由它的无符号拉普拉斯谱所确定的. 相似文献
15.
设$k$是正整数, $G$是一个边数给定的简单无向图, 其边数$m\ge 2k$, 最大度$\Delta(G)\le m-k$, 本文给出了图$G$的无符号拉普拉斯谱半径$q(G)$的一个上界. 对边数为$m\ge 8$的两个连通图$G_1$和$G_2$, 利用这个上界我们证明了一个排序定理: 如果$\Delta(G_1)>\Delta(G_2)+1$ 且 $\Delta(G_1)\ge \frac{m}{2}+2$, 那么$q(G_1)>q(G_2)$. 对于不含三角形的图, 我们得到两个更强的结果. 作为上述排序定理的一个应用, 我们完全刻画了无符号拉普拉斯谱半径最大的围长为$c$的$m$边图, 其中$m\ge \max\{ 2c, c+9\}$, 部分解决了陈雯雯等人在[Linear Algebra Appl. 645(2022)123-136]上提出的一个公开问题. 相似文献
16.
Xiao-Dong Zhang 《Discrete Applied Mathematics》2009,157(13):2928-2937
In this paper, we investigate the properties of the largest signless Laplacian spectral radius in the set of all simple connected graphs with a given degree sequence. These results are used to characterize the unicyclic graphs that have the largest signless Laplacian spectral radius for a given unicyclic graphic degree sequence. Moreover, all extremal unicyclic graphs having the largest signless Laplacian spectral radius are obtained in the sets of all unicyclic graphs of order n with a specified number of leaves or maximum degree or independence number or matching number. 相似文献
17.
图G的Pebbling数f(G)是最小的正整数n,使得不论n个Pebble如何放置在G的顶点上,总可以通过一系列的Pebbling移动把1个Pebble移到任意一点上,其中Pebbling移动是从一个顶点处移走两个Pebble而把其中一个移到与其相邻的一个顶点上.Graham猜测对于任意的连通图G和H有f(G×H)≤f(G)f(H).本文证明对于一个完全γ部图和一个具有2-Pebbleing性质的图来说,Graham猜想成立.作为一个推论,当G和H均为完全γ部图时,Graham猜想成立. 相似文献