有低最大平均度的图的(2,1)-全标号

The(2,1)-total labeling of graphs with low maximum average degree

图G的最大平均度mad(G)是其所有真子图的平均度的最大值,即mad(G)=max{(2|E(H)|)/(|V(H)|)},H■G.文中证明了:若G为连通图,△(G)≤3,mad(G)<9/4,则λ_2~T(G)≤5.若G为连通图,△(G)≤4,mad(G)<5/2,则λ_2~T(G)≤7.

The maximum average degree of graph G,denoted by mad(G),is the maximum value of the average degree of all its real subgraph,so mad(G) = max{_(|V(H)|)/^(2|E(H)|),H■G.It is proved that if G was a connected graph,△(G) ≤ 3,mad(G) <9/4,thenλ_2~T(G)≤5,and if G is a connected graph,△(G)≤4,mad(G) <5/2,thenλ_2~T(G)≤7.