共查询到20条相似文献,搜索用时 3 毫秒
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Daniel Kotlar 《Graphs and Combinatorics》2016,32(3):1027-1038
Let G be a complete k-partite simple undirected graph with parts of sizes \(p_1\le p_2\cdots \le p_k\). Let \(P_j=\sum _{i=1}^jp_i\) for \(j=1,\ldots ,k\). It is conjectured that G has distance magic labeling if and only if \(\sum _{i=1}^{P_j} (n-i+1)\ge j{{n+1}\atopwithdelims (){2}}/k\) for all \(j=1,\ldots ,k\). The conjecture is proved for \(k=4\), extending earlier results for \(k=2,3\). 相似文献
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Let G be a graph with vertex set V (G), edge set E(G) and maximum degree Δ respectively. G is called degree-magic if it admits a labelling of the edges by integers {1, 2, …,|E(G)|} such that for any vertex v the sum of the labels of the edges incident with v is equal to (1+|E(G)|)/2·d(v), where d(v) is the degree of v. Let f be a proper edge coloring of G such that for each vertex v ∈ V (G),|{e:e ∈ Ev, f(e) ≤ Δ/2}|=|{e:e ∈ Ev, f(e) > Δ/2}|, and such an f is called a balanced edge coloring of G. In this paper, we show that if G is a supermagic even graph with a balanced edge coloring and m ≥ 1, then (2m + 1)G is a supermagic graph. If G is a d-magic even graph with a balanced edge coloring and n ≥ 2, then nG is a d-magic graph. Results in this paper generalise some known results. 相似文献
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图G的L(2,1)-标号是一个从顶点V(G)集到非负整数集的函数f(x),使得若d(x,y):1,则|f(x)-f(y)|≥2;若d(x,y)=2,则|f(x)-f(y)|≥1。图G的L(2,1)-标号数A(G)是使得G有max{f(v):v∈V(G)}=k的L(2,1)-标号中的最小数愚。本文将L(2,1)-标号问题推广到更一般的情形即L(d1,d2,d3)-标号问题,并得出了复合图的λd1,d2,d3(G)的上界。 相似文献
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Sylwia Cichacz 《Graphs and Combinatorics》2014,30(3):565-571
A group distance magic labeling or a ${\mathcal{G}}$ -distance magic labeling of a graph G = (V, E) with ${|V | = n}$ is a bijection f from V to an Abelian group ${\mathcal{G}}$ of order n such that the weight ${w(x) = \sum_{y\in N_G(x)}f(y)}$ of every vertex ${x \in V}$ is equal to the same element ${\mu \in \mathcal{G}}$ , called the magic constant. In this paper we will show that if G is a graph of order n = 2 p (2k + 1) for some natural numbers p, k such that ${\deg(v)\equiv c \mod {2^{p+1}}}$ for some constant c for any ${v \in V(G)}$ , then there exists a ${\mathcal{G}}$ -distance magic labeling for any Abelian group ${\mathcal{G}}$ of order 4n for the composition G[C 4]. Moreover we prove that if ${\mathcal{G}}$ is an arbitrary Abelian group of order 4n such that ${\mathcal{G} \cong \mathbb{Z}_2 \times\mathbb{Z}_2 \times \mathcal{A}}$ for some Abelian group ${\mathcal{A}}$ of order n, then there exists a ${\mathcal{G}}$ -distance magic labeling for any graph G[C 4], where G is a graph of order n and n is an arbitrary natural number. 相似文献
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将无向图距离标号边跨度的概念引入到有向图.运用图的流(flow)及tension理论,确定了有向树和有向圈的边跨度,以及最长有向路长不超过3的有向二部图边跨度的可达上下界. 相似文献
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YanLiu 《应用数学学报(英文版)》2004,20(4):641-646
The maximum matching graph of a graph has a vertex for each maximum matching and an edge for each pair of maximum matchings which differ by exactly one edge. In this paper, we obtain a lower bound of distance between two vertices of maximum matching graph, and give a necessary and sufficient condition that the bound can be reached. 相似文献
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Let G = (V, E) be a graph. A mapping f: E(G) → {0, l} m is called a mod 2 coding of G, if the induced mapping g: V(G) → {0, l} m , defined as \(g(v) = \sum\limits_{u \in V,uv \in E} {f(uv)}\) , assigns different vectors to the vertices of G. Note that all summations are mod 2. Let m(G) be the smallest number m for which a mod 2 coding of G is possible. Trivially, m(G) ≥ ?Log2 |V|?. Recently, Aigner and Triesch proved that m(G) ≤ ?Log2 |V|? + 4. In this paper, we determine m(G). More specifically, we prove that if each component of G has at least three vertices, then $$mG = \left\{ {\begin{array}{*{20}c} {k,} & {if \left| V \right| \ne 2^k - 2} \\ {k + 1,} & {else} \\ \end{array} ,} \right.$$ where k = ?Log2 |V|?. 相似文献
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An antimagic labeling of a graph G is a one‐to‐one correspondence between and such that the sum of the labels assigned to edges incident to distinct vertices are different. If G has an antimagic labeling, then we say G is antimagic. This article proves that cubic graphs are antimagic. 相似文献
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A graph is antimagic if there is a one‐to‐one correspondence such that for any two vertices , . It is known that bipartite regular graphs are antimagic and nonbipartite regular graphs of odd degree at least three are antimagic. Whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. In this article, we solve this problem and prove that all even degree regular graphs are antimagic. 相似文献
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Doklady Mathematics - New bounds on the modularity of distance graphs were obtained and the exact value of modularity was calculated for G(n, 2, 1) graphs. 相似文献
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A graph G on n vertices is a tight distance graph if there exists a set such that and if and only if . A characterization of the degree sequences of tight distance graphs is given. This characterization yields a fast method for recognizing and realizing degree sequences of tight distance graphs. 相似文献
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Mathematical Notes - For positive integers n > r > s, G(n, r, s) is the graph whose vertices are the r-element subsets of an n-element set, two subsets being adjacent if their... 相似文献