The Edge-bandwidth of a Tree and its Number of Leaves
DU Xianyun
REN Qiudao
WEN Huayan
Abstract：A label f of an edge in a graph G refers to one-mapping from the edge set E(G)to the set{1, 2,…,m},namely:e∈E(G),t,1≤t≤m,satisying f(e)= t.The edge-bandwidth of a graph B'(G)= minBf'(G),wherein Bf'(G)= max{ | f(uv)-f(uw)| :uv,uw∈E(G)}.The paper obtains that the ine-qualities「(m-1)/(d-1)┐≤B'(T)≤l-s,0≤s≤l/ 2,wherein d is the diameter of a tree and l is the number of its leaves.Moreover the edge-bandwidth of a k(even)-regular tree T satisfies the inequalities B'(T)≤l/ 2,and the edge-bandwidth of a generalized star graph T* does B'(T*)= l or l-1.
Keywords：independent adjacent edge- setedge bandwidthtreenumber of leaves
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：5( 1-4,19 )