Delta-Optimum Exclusive Sum Labeling of Certain Graphs with Radius One
Delta-Optimum Exclusive Sum Labeling of Certain Graphs with Radius One
复制标题
某些半径为一的图的Delta最优异和标记
DOI：
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发表时间：
2003
期刊：
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通讯作者：
Mirka Miller
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文献类型：
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作者：
Mauritsius Tuga;Mirka Miller
一个映射L称为图H(V(H)，E(H))的和标号，如果它是从V(H)到一组正整数的注入，使得xy∈E(H)当且仅当存在一个顶点w∈V(H)使得L(W)=L(X)+L(Y).在这种情况下，w称为工作顶点。定义L为图G的一个独占和标号，如果它是$Gcuar K_{r}$对某个非负整数r的和标号，且G不含工作点。一般说来，图G需要对一些孤立的顶点进行独占标记。这样的孤立顶点的最小可能数目称为G的独占和数；表示为e(G)。
图G的独占和标号称为最优的，如果它用e(G)孤立点独占地标号G。如果e(G)=Δ(G)，其中Δ(G)表示G中顶点的最大次数，这种标号称为Δ-最优排他和标号。
本文给出了一类半径为1的图的Δ-最优排他和标号，即将一个整和图的所有顶点连接到另一个顶点所得到的图。这类图包含无限多个图，其中包括一些更常见的图，如轮子图、扇形图、友谊图、广义友谊图和多锥图。
A mapping L is called a sum labeling of a graph H(V(H),E(H)) if it is an injection from V(H) to a set of positive integers, such that xy ∈ E(H) if and only if there exists a vertex w ∈ V(H) such that L(w) = L(x) + L(y). In this case, w is called a working vertex. We define L as an exclusive sum labeling of a graph G if it is a sum labeling of $Gcupar K_{r}$ for some non negative integer r, and G contains no working vertex. In general, a graph G will require some isolated vertices to be labeled exclusively. The least possible number of such isolated vertices is called exclusive sum number of G; denoted by e(G).
An exclusive sum labeling of a graph G is said to be optimum if it labels G exclusively by using e(G) isolated vertices. In case e (G) = Δ (G), where Δ(G) denotes the maximum degree of vertices in G, the labeling is called Δ-optimum exclusive sum labeling.
In this paper we present Δ-optimum exclusive sum labeling of certain graphs with radius one, that is, graphs which can be obtained by joining all vertices of an integral sum graph to another vertex. This class of graphs contains infinetely many graphs including some populer graphs such as wheels, fans, friendship graphs, generalised friendship graphs and multicone graphs.