The Strong 3-rainbow Index of Comb Product of a Tree and a Connected Graph

• Zata, Yumni Awanis

• A.N.M., Salman

• Suhadi, Wido Saputro

抄録

Let G be a nontrivial connected graph of order n. Let k be an integer with 2 ≤ k ≤ n. A strong k-rainbow coloring of G is an edge-coloring of G having property that for every set S of k vertices of G, there exists a tree with minimum size containing S whose all edges have distinct colors. The minimum number of colors required such that G admits a strong k-rainbow coloring is called the strong k-rainbow index srxk(G) of G. In this paper, we study the strong 3-rainbow index of comb product between a tree and a connected graph, denoted by Tn⊳o H. Notice that the size of Tn⊳o H is the trivial upper bound for srx3(Tn⊳o H), which means we can assign distinct colors to all edges of Tn⊳o H. However, there are some connected graphs H such that some edges of Tn⊳o H may be colored the same. Therefore, in this paper, we characterize connected graphs H with srx3(Tn⊳o H) =

Let G be a nontrivial connected graph of order n. Let k be an integer with 2 ≤ k ≤ n. A strong k-rainbow coloring of G is an edge-coloring of G having property that for every set S of k vertices of G, there exists a tree with minimum size containing S whose all edges have distinct colors. The minimum number of colors required such that G admits a strong k-rainbow coloring is called the strong k-rainbow index srxk(G) of G. In this paper, we study the strong 3-rainbow index of comb product between a tree and a connected graph, denoted by Tn⊳o H. Notice that the size of Tn⊳o H is the trivial upper bound for srx3(Tn⊳o H), which means we can assign distinct colors to all edges of Tn⊳o H. However, there are some connected graphs H such that some edges of Tn⊳o H may be colored the same. Therefore, in this paper, we characterize connected graphs H with srx3(Tn⊳o H) =

収録刊行物

• 情報処理学会論文誌

  情報処理学会論文誌 61 (12), 2020-12-15

キーワード

• [特集：離散と計算の幾何・グラフ・ゲーム] comb product, rainbow coloring, strong k-rainbow index

詳細情報

• CRID: 1050006297339203712
• NII論文ID: 170000184195
• NII書誌ID: AN00116647
• ISSN: 18827764
• Web Site: http://id.nii.ac.jp/1001/00208726/
• 本文言語コード: en
• 資料種別: journal article
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