Wn⊙Pm和Cn⊙Sm的r-hued染色

唐夢(mèng)　劉鳳霞

摘要：圖G和H的Corona乘積圖記為G⊙H，它是復(fù)制一個(gè)圖G以及復(fù)制|V（G）|個(gè)圖H，把圖G的第i個(gè)頂點(diǎn)跟復(fù)制的第i個(gè)圖H的每個(gè)頂點(diǎn)相連.圖G的（k，r）-染色是用k種顏色對(duì)圖G進(jìn)行正常染色，使得點(diǎn)v的所有鄰點(diǎn)至少染min{r，d（v）}種不同的顏色，其中d（v）是圖G中頂點(diǎn)v的度數(shù).把圖G的具有（k，r）-染色的最小正整數(shù)k稱為r-hued色數(shù)，用χ_r（G）表示，通過對(duì)r-hued染色的定義，得到W_n⊙P_m和C_n⊙S_m的r-hued色數(shù).

關(guān)鍵詞：（k，r）-染色; r-hued色數(shù); Corona乘積圖

中圖分類號(hào)：O157.5 文獻(xiàn)標(biāo)志碼：A 文章編號(hào)：1001-8395（2023）05-0646-06

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On r-hued Coloring of W_n⊙P_mand? C_n⊙S_mTANG Meng，LIU Fengxia（College of Mathematics and System Science， Xinjiang University， Urumqi 830046， Xinjiang）

Abstract：The Corona product graph of two graphs G and H is denoted by G⊙H， which is obtained by taking one copy of G and |V（G）| copies of H where ith vertex of G is adjacent to every vertex in the ith copy of H . A （k，r）-coloring of a graph G is a proper k-coloring of graph G such that the neighbors of any vertex v receive at least min {r，d（v）} different colors， where d（v） is the degree of vertex v of graph G. The smallest integer k such that G has a （k，r）-coloring is called the r-hued chromatic number and denoted by χr（G）. By the definitions of r-hued coloring， the r-hued chromatic number of W_n⊙P_mand C_n⊙S_mare obtained.

Keywords：（k，r）-coloring; r-hued chromatic number; Corona product of graphs

2020 MSC：05C15（編輯余毅）