调和平衡图直径与顶点数的关系

Harmonic Even Graph

如果非平凡连通图G中任意的顶点v都对应G中唯一的顶点,使d(v,)=diam(G),则称G为平衡图.若平衡图G中由边uv∈B(G)可推出∈B(G),则称G为调和平衡图.本文证明了顶点数为n直径为d(d≥5)的调和平衡图G当G≌C_n时有关系式n≥3d.

A nontrivial connected graph G is called even if for each vertex v of G there is an unique vertex such that d(v, )=diam(G).In particular,an even graph G is called harmonic if ∈E(G) whenever uv∈ E(G).For a harmonic even graph other than an even cycle of order n and diameter d(d≥5) it is shown that n≥3d.