竖梯的局部替换图的L(d,1,1)-标号  

The L(d,1,1)-Labeling of the Local-Replacements of the Vertical Ladders

作　　者：刘跃芹 吕大梅[1] LIU Yue-qin;LU Da-mei(School of Science,Nantong University,Nantong 226007,China)

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《数学的实践与认识》2023年第4期267-271,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11371207);江苏省自然科学青年基金(BK20140424);南通大学校级基金(14ZY009);南通大学大学生创新训练计划项目(2019030)。

摘　　要：图的L(d,1,1)-标号定义为顶点集V(G)到非负整数集的映射f,且当d(u,v)=1时,均有|f(u)-f(v)|≥d,当d(u,v)=2,3时,均有|f(u)-f(v)|≥1.不妨设0为最小标号,则称图G的所有L(d,1,1)-标号中的最大跨度max{f(v):v∈V(G)}的最小数为图的L(d,1,1)-标号数,记为λd(G).基本给出了竖梯的局部替换图的L(d,1,1)-标号数的确切值或界.An L(d,1,1)-labeling of a graph is a mapping f from the vertex set V(G)to the set of all nonnegative integers such that |f(u)-f(v)|≥d if d(u,v)=1,|f(u)-f(v)|≥1 if d(u,v)=2,3.Without loss of generality,let the minimum label be 0,then the L(d,1,1)-labeling number λd(G)of a graph G is the minimum number of the span max{f(v):v∈V(G)}under all the L(d,1,1)-labeling of G.In this paper,the L(d,1,1)-labeling number of the local-replacements of the vertical ladders is given.

关 键 词：L(d 1 1)-标号 L(d 1 1)-标号数 Cartesian积 替换图 

分 类 号：O157.5[理学—数学]