The Gracefulness and Balance of Some Unicyclic Graphs
Xiang-Feng Pan · Journal of Hefei University · 2008
Let L be a vertex label of simple graph G,L is said to be a graceful label of G if L satisfies both the following:(1) L is an injective mapping from V(G) to{0,1,2,…,|E|};(2) the function L′ obtained by setting L′=(e)=|L(u)-L(v)|,where e=uv is an objective function from E(G) to {0,1,2,…,|E|}.Furthermore,if there is an integer c for each uv∈E(G),either L(u)≤cL(v) or L(v)≤cL(u),then L is said to be a balanced label of G,and its feature is c.In this paper,we put focus on the balance of some unicyclic graphs,and give their balance label as well as their features.