Abstract
In this paper we introduce the notion of λ- edge span of a graph, where λ is the λ -number or L(2; 1) labeling number of a graph. Also, we introduce the concept of almost regularness for infinite graphs. An infinite graph is almost regular if it is regular except for a finite number of points. Here, we consider some important infinite graphs which are al-most regular and find the λ -number and λ -edge span of them.