Neighbor Sum Distinguishing Chromatic Index of Sparse Graphs via the Combinatorial Nullstellensatz
Let Ф ： E（G）→ {1, 2,…, k}be an edge coloring of a graph G. A proper edge-k-coloring of G is called neighbor sum distinguishing if ∑eЭu Ф（e）≠∑eЭu Ф（e） for each edge uv∈E（G）.The smallest value k for which G has such a coloring is denoted by χ＇Σ（G） which makes sense for graphs containing no isolated ed...
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| Veröffentlicht in: | Acta Mathematicae Applicatae Sinica 2018, Vol.34 (1), p.135-144 |
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| creator | Yu, Xiao-wei Gao, Yu-ping Ding, Lai-hao |
| description | Let Ф ： E（G）→ {1, 2,…, k}be an edge coloring of a graph G. A proper edge-k-coloring of G is called neighbor sum distinguishing if ∑eЭu Ф（e）≠∑eЭu Ф（e） for each edge uv∈E（G）.The smallest value k for which G has such a coloring is denoted by χ＇Σ（G） which makes sense for graphs containing no isolated edge（we call such graphs normal）. It was conjectured by Flandrin et al. that χ＇Σ（G） ≤△（G） ＋ 2 for all normal graphs,except for C5. Let mad（G） = max{（2｜E（H）｜）/（｜V（H）｜）｜HЭG}be the maximum average degree of G. In this paper,we prove that if G is a normal graph with△（G）≥5 and mad（G） 〈 3-2/（△（G））, then χ＇Σ（G）≤△（G） ＋ 1. This improves the previous results and the bound △（G） ＋ 1 is sharp. |
| doi_str_mv | 10.1007/s10255-018-0731-4 |
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This improves the previous results and the bound △（G） ＋ 1 is sharp.</description><edition>English series</edition><identifier>ISSN: 0168-9673</identifier><identifier>EISSN: 1618-3932</identifier><identifier>DOI: 10.1007/s10255-018-0731-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Combinatorial analysis ; Graph coloring ; Graphs ; Math Applications in Computer Science ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Theoretical</subject><ispartof>Acta Mathematicae Applicatae Sinica, 2018, Vol.34 (1), p.135-144</ispartof><rights>Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c343t-f940ede690bb7d1cef1b479b8a8c32a90d387ebc6467e23609ce1805eb2b50073</citedby><cites>FETCH-LOGICAL-c343t-f940ede690bb7d1cef1b479b8a8c32a90d387ebc6467e23609ce1805eb2b50073</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/85829X/85829X.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10255-018-0731-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10255-018-0731-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,4010,27900,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Yu, Xiao-wei</creatorcontrib><creatorcontrib>Gao, Yu-ping</creatorcontrib><creatorcontrib>Ding, Lai-hao</creatorcontrib><title>Neighbor Sum Distinguishing Chromatic Index of Sparse Graphs via the Combinatorial Nullstellensatz</title><title>Acta Mathematicae Applicatae Sinica</title><addtitle>Acta Math. Appl. Sin. Engl. Ser</addtitle><addtitle>Acta Mathematicae Applicatae Sinica</addtitle><description>Let Ф ： E（G）→ {1, 2,…, k}be an edge coloring of a graph G. A proper edge-k-coloring of G is called neighbor sum distinguishing if ∑eЭu Ф（e）≠∑eЭu Ф（e） for each edge uv∈E（G）.The smallest value k for which G has such a coloring is denoted by χ＇Σ（G） which makes sense for graphs containing no isolated edge（we call such graphs normal）. It was conjectured by Flandrin et al. that χ＇Σ（G） ≤△（G） ＋ 2 for all normal graphs,except for C5. Let mad（G） = max{（2｜E（H）｜）/（｜V（H）｜）｜HЭG}be the maximum average degree of G. In this paper,we prove that if G is a normal graph with△（G）≥5 and mad（G） 〈 3-2/（△（G））, then χ＇Σ（G）≤△（G） ＋ 1. This improves the previous results and the bound △（G） ＋ 1 is sharp.</description><subject>Applications of Mathematics</subject><subject>Combinatorial analysis</subject><subject>Graph coloring</subject><subject>Graphs</subject><subject>Math Applications in Computer Science</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><issn>0168-9673</issn><issn>1618-3932</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOD5-gLug6-rNY5J2KeMTRBej65B0bqeRTjMmrai_3gwjunN1uXC-c-Aj5ITBOQPQF4kBn04LYGUBWrBC7pAJU_kTleC7ZAJMlUWltNgnBym9AjAtlJ4Q94h-2boQ6Xxc0SufBt8vR5_afOisjWFlB1_T-36BHzQ0dL62MSG9jXbdJvruLR1apLOwcr63Q4jedvRx7Lo0YNdhn-zwdUT2GtslPP65h-Tl5vp5dlc8PN3ezy4filpIMRRNJQEXqCpwTi9YjQ1zUleutGUtuK1gIUqNrlZSaeRCQVUjK2GKjrtpViAOydm2dx3D24hpMK9hjH2eNBwYZ5IrUeYU26bqGFKK2Jh19CsbPw0Ds1FptipNVmk2Ko3MDN8yKWf7Jca_5v-g05-hNvTLt8z9LiktOZdMgfgGFkyCrQ</recordid><startdate>2018</startdate><enddate>2018</enddate><creator>Yu, Xiao-wei</creator><creator>Gao, Yu-ping</creator><creator>Ding, Lai-hao</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2018</creationdate><title>Neighbor Sum Distinguishing Chromatic Index of Sparse Graphs via the Combinatorial Nullstellensatz</title><author>Yu, Xiao-wei ; Gao, Yu-ping ; Ding, Lai-hao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-f940ede690bb7d1cef1b479b8a8c32a90d387ebc6467e23609ce1805eb2b50073</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applications of Mathematics</topic><topic>Combinatorial analysis</topic><topic>Graph coloring</topic><topic>Graphs</topic><topic>Math Applications in Computer Science</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yu, Xiao-wei</creatorcontrib><creatorcontrib>Gao, Yu-ping</creatorcontrib><creatorcontrib>Ding, Lai-hao</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><jtitle>Acta Mathematicae Applicatae Sinica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yu, Xiao-wei</au><au>Gao, Yu-ping</au><au>Ding, Lai-hao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Neighbor Sum Distinguishing Chromatic Index of Sparse Graphs via the Combinatorial Nullstellensatz</atitle><jtitle>Acta Mathematicae Applicatae Sinica</jtitle><stitle>Acta Math. Appl. Sin. Engl. Ser</stitle><addtitle>Acta Mathematicae Applicatae Sinica</addtitle><date>2018</date><risdate>2018</risdate><volume>34</volume><issue>1</issue><spage>135</spage><epage>144</epage><pages>135-144</pages><issn>0168-9673</issn><eissn>1618-3932</eissn><abstract>Let Ф ： E（G）→ {1, 2,…, k}be an edge coloring of a graph G. A proper edge-k-coloring of G is called neighbor sum distinguishing if ∑eЭu Ф（e）≠∑eЭu Ф（e） for each edge uv∈E（G）.The smallest value k for which G has such a coloring is denoted by χ＇Σ（G） which makes sense for graphs containing no isolated edge（we call such graphs normal）. It was conjectured by Flandrin et al. that χ＇Σ（G） ≤△（G） ＋ 2 for all normal graphs,except for C5. Let mad（G） = max{（2｜E（H）｜）/（｜V（H）｜）｜HЭG}be the maximum average degree of G. In this paper,we prove that if G is a normal graph with△（G）≥5 and mad（G） 〈 3-2/（△（G））, then χ＇Σ（G）≤△（G） ＋ 1. 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| subjects | Applications of Mathematics Combinatorial analysis Graph coloring Graphs Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| title | Neighbor Sum Distinguishing Chromatic Index of Sparse Graphs via the Combinatorial Nullstellensatz |
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