| 关于图P_n~k的均匀染色 |
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| 引用本文： | 原新生,严谦泰.关于图P_n~k的均匀染色[J].数学的实践与认识,2005(4). |
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| 作者姓名： | 原新生 严谦泰 |
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| 作者单位： | 安阳师范学院数学系 河南安阳455002
(原新生)，安阳师范学院数学系 河南安阳455002(严谦泰) |
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| 摘 要： | 对简单图G=〈V,E〉及自然数k,令V(Gk) =V(G) ,E(Gk) =E(G)∪{uv|d(u,v) =k},其中d(u,v)表示G中u,v的距离,称图Gk为G的k方图.本文讨论了路的k方图Pkn的均匀点染色、均匀边染色和均匀邻强边染色,利用图的色数的基本性质和构造染色函数的方法,得到相应的色数χev(Pkn) ,χ′ee(Pkn) ,χ′eas(Pkn) .并证明猜想“若图G有m -EASC,则一定有m +1 -EASC”对Pkn是正确的.
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| 关 键 词： | 图 均匀点染色 均匀边染色 均匀邻强边染色 |
On The Equitable Coloring of P_n~k |
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| YUAN Xin-sheng,YAN Qian-tai.On The Equitable Coloring of P_n~k[J].Mathematics in Practice and Theory,2005(4). |
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| Authors: | YUAN Xin-sheng YAN Qian-tai |
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| Abstract: | Let G= be a simple graph and k be a nature number, we defined graph Gk, V(Gk)=V(G), E(Gk)=E(G)∪{uv|d(u, v)=k}, here d(u,v) is the distance of u, v, Gk is called k-power graph of G. In this paper, we study equitable vertex coloring, equitable edge coloring and equitable adjacent strong edge coloring of Pk_n. We obtained χ_ ev(Pk_n), χ′_ ee(Pk_n) and χ′_ eas(Pk_n). We proved the conjecture, that if graph G has m-EASC then it has m+1-EASC, is right for Pk_n. |
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| Keywords: | graph equitable vertex coloring equitable edge coloring equitable adjacent strong edge coloring |
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