<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mi>D</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced><mtext> </mtext></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/42055F53-AE32-4b0b-A95D-B58439E41972-M002.jpg"><?fx-imagestate width="11.51466751" height="5.07999992"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/42055F53-AE32-4b0b-A95D-B58439E41972-M002c.jpg"><?fx-imagestate width="11.51466751" height="5.07999992"?></graphic></alternatives></inline-formula>-vertex sum distinguishing edge coloring of tricyclic graph

BAI Yu; QIANG Huiying; HE Jing

doi:10.11714/acta.snus.ZR20240177

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D (2)

-vertex sum distinguishing edge coloring of tricyclic graph

Research articles | 更新时间：2026-03-18

- $D (2)$ -vertex sum distinguishing edge coloring of tricyclic graph
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 65, Issue 2, Pages: 160-172(2026)
- 作者机构：
  
  兰州交通大学数理学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.11714/acta.snus.ZR20240177
  CLC： O157.5
- Received：27 May 2024，
  
  Revised：2025-12-15，
  
  Accepted：15 December 2025，
  
  Online First：30 January 2026，
  
  Published：25 March 2026
- 稿件说明：
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白羽,强会英,何静.三圈图的D2 -点和可区别边染色[J].中山大学学报(自然科学版)(中英文),2026,65(02):160-172.

BAI Yu,QIANG Huiying,HE Jing.D2 -vertex sum distinguishing edge coloring of tricyclic graph[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(02):160-172.
白羽,强会英,何静.三圈图的D2 -点和可区别边染色[J].中山大学学报(自然科学版)(中英文),2026,65(02):160-172. DOI： 10.11714/acta.snus.ZR20240177.

BAI Yu,QIANG Huiying,HE Jing.D2 -vertex sum distinguishing edge coloring of tricyclic graph[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(02):160-172. DOI： 10.11714/acta.snus.ZR20240177.

D (2)

-vertex sum distinguishing edge coloring of tricyclic graph

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摘要

利用拆分法和构造具体染色法，证明了树高为0的三圈图的

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7.45066643

3.21733332

-点和可区别的边染色. 其次，利用分析法、反证法以及组合零点定理证明了树高不为0，且不含4种特殊子图的三圈图的

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102119305&type=

7.45066643

3.21733332

-点和可区别的边染色，并给出了此类图的

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102119305&type=

7.45066643

3.21733332

-点和可区别边色数的一个上界.

Abstract

By using the splitting method and constructing specific coloring methods，we proved the

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102119315&type=

8.63599968

3.80999994

-vertex sum distinguishing edge coloring of a tricyclic graph with zero tree height. Secondly， we proved the

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102119315&type=

8.63599968

3.80999994

-vertex sum distinguishing edge coloring of a tricyclic graph with non zero tree height and without four special subgraphs using analytic method， proof of contradiction， and Combinatorial Nullstellensatz. And provided an upper bound on the

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102119315&type=

8.63599968

3.80999994

-vertex sum distinguishing edge coloring of this type of graphs.

关键词

Keywords

references

陈媛媛，王国平， 2019 . 三圈图的无符号拉普拉斯谱半径［J］. 运筹学学报， 23 （ 1 ）： 81 - 89 .

刘欢，强会英，王洪申， 2024a . 单圈图的 <math id="M1199"><mi>D</mi><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn></mrow></mfenced></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121201&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121185&type= 6.77333355 3.21733332 -点和可区别边染色［J］. 南开大学学报（自然科学版）， 57 （ 1 ）： 91 - 97 .

刘欢，强会英，王洪申，等， 2024b . 树图的 <math id="M1200"><mn mathvariant="normal">2</mn></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121171&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121215&type= 1.60866666 2.28600001 -距离和可区别染色［J］. 山东大学学报（理学版）， 59 （ 2 ）： 47 - 52+58 .

强会英，姚丽， 2021 . 无 <math id="M1201"><msub><mrow><mi>K</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121202&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121186&type= 3.04800010 3.21733332 -子式图的 <math id="M1202"><mn mathvariant="normal">2</mn></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121171&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121215&type= 1.60866666 2.28600001 -距离和可区别边染色［J］. 山东大学学报（理学版）， 56 （ 11 ）： 83 - 86 .

邵淑宏， 2021 . 随机图的 <math id="M1203"><mi>D</mi><mfenced separators="|"><mrow><mi>β</mi></mrow></mfenced></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121172&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=102121216&type= 7.28133297 3.80999994 -点和可区别边染色及边幻和标号的算法研究［D］. 兰州：兰州交通大学 .

谭钧铭， 2022 . 几类圈图的邻和可区别染色［D］. 兰州：兰州交通大学 .

张忠辅，李敬文，陈祥恩，等， 2006 . 图的距离不大于 β 的任意两点可区别的边染色［J］. 数学学报， 49 （ 3 ）： 703 - 708 .

FLANDRIN E ， MARCZYK A ， PRZYBYŁO J ， et al ， 2013 . Neighbor sum distinguishing index ［J］. Graphs Comb ， 29 （ 5 ）： 1329 - 1336 .

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D2 -vertex sum distinguishing edge coloring of tricyclic graph

DOI：10.11714/acta.snus.ZR20240177

摘要

Abstract

关键词

Keywords

references

$D (2)$ -vertex sum distinguishing edge coloring of tricyclic graph