The Multi-level Distance Labeling For Several Classes Of Tree Graphs

The multi-level distance labeling for a connected graph G also calls the radio labeling. It is a mappin f:V(G)â†'{0,1,2,…}, so that the following is satisfied for u, v∈V(G):|f(u)-f(v)|≥diam(G)+1-d(u,v), where diam(G) is the diameter of G, d(u,v) is the distance between u,v. The span of f is defined as max{f(u)-f(v)} u,v∈V(G). The multi-level distance number of a graph G is the minimum span of all multi-level distance labelings for G.A class of symmetric binary trees about root, symmetric lobster trees about weight center and symmetric spiders trees about weight center are investigated, and their lower bounds of the multi-level distance number are obtained, and then the exact numbers in some special cases of the multi-level distance number are obtained.This paper is composed of three parts:in the first part, it is introduced that the multi-level distance labeling of symmetric binary trees about root, and given that l≤6) the exact number of multi-level distance number,In the second part, it is studied that the multi-level distance labeling of symmetric lobster trees about weight center, and obtained that the exact number of multi-level distance number of Lk,(t3,…,ti,…,tk-2),In the third part, it is mainly discussed that the multi-level distance labeling of symmetric spider-like trees about weight center, And give SL3nlm the exact number of multi-level distance number. rn(SL3nlm)=3mnl2-3nl2-6mnl+3mn+12nl-6n+1.