三正则连通图与圈的并图Cordial性

数学季刊 ›› 2010, Vol. 25 ›› Issue (2): 244-248.

三正则连通图与圈的并图Cordial性

1. Department of Mathematics, Yang-en University2. College of Mathematics and Information Science, Henan University

收稿日期:2008-06-01 出版日期:2010-06-30 发布日期:2023-06-05
作者简介:XIE Yan-tao(1980-), male, native of Pingdingshan, Henan, M.S.D., engages in graph theory and combinatorial oppimization; CHE Ying-tao(1981-), male, native of Linying, Henan, M.S.D., engages in graph theory and combinatorial oppimization.
基金资助:

The Cordiality on the Union of 3-regular Connected Graph and Cycle

1. Department of Mathematics, Yang-en University2. College of Mathematics and Information Science, Henan University

Received:2008-06-01 Online:2010-06-30 Published:2023-06-05
About author:XIE Yan-tao(1980-), male, native of Pingdingshan, Henan, M.S.D., engages in graph theory and combinatorial oppimization; CHE Ying-tao(1981-), male, native of Linying, Henan, M.S.D., engages in graph theory and combinatorial oppimization.

摘要/Abstract

摘要： Diab proved the following graphs are Cordial; P_mK_1,n if and only if (m,n) =(1,2); C_mK_1,n; P_mK_n; C_mK_n for all m and n except m≡2(mod 4). In this paper, we proved the Cordiality on the union of 3-regular connected graph K₃ and cycle C_m. First we have the Lemma 2, if uv∈ E(G), G is Cordial, we add 4 vertices x, y, z, w in sequence to the edge uv, obtain a new graph denoted by G*, then G* is still Cordial, by this lemma, we consider four cases on the union of 3-regular connected graph R₃, and for every case we distinguish four subcases on the cycle C_m.

关键词: 3-regular graph, Cordial graph, union graph

Abstract: Diab proved the following graphs are Cordial; P_mK_1,n if and only if (m,n) =(1,2); C_mK_1,n; P_mK_n; C_mK_n for all m and n except m≡2(mod 4). In this paper, we proved the Cordiality on the union of 3-regular connected graph K₃ and cycle C_m. First we have the Lemma 2, if uv∈ E(G), G is Cordial, we add 4 vertices x, y, z, w in sequence to the edge uv, obtain a new graph denoted by G*, then G* is still Cordial, by this lemma, we consider four cases on the union of 3-regular connected graph R₃, and for every case we distinguish four subcases on the cycle C_m.

Key words: 3-regular graph, Cordial graph, union graph

中图分类号:

O157.5

谢炎涛, 车颍涛, 刘峙山. 三正则连通图与圈的并图Cordial性[J]. 数学季刊, 2010, 25(2): 244-248.

XIE Yan-tao, CHE Ying-tao, LIU Zhi-shan. The Cordiality on the Union of 3-regular Connected Graph and Cycle [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(2): 244-248.