{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T16:56:16Z","timestamp":1775062576286,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Project of Natural Science Foundation of Gansu Province, China","award":["24JRRA222"],"award-info":[{"award-number":["24JRRA222"]}]},{"name":"Key Project of Natural Science Foundation of Gansu Province, China","award":["25JRRA805"],"award-info":[{"award-number":["25JRRA805"]}]},{"name":"Foundation for Innovative Fundamental Research Group Project of Gansu Province","award":["24JRRA222"],"award-info":[{"award-number":["24JRRA222"]}]},{"name":"Foundation for Innovative Fundamental Research Group Project of Gansu Province","award":["25JRRA805"],"award-info":[{"award-number":["25JRRA805"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A neighbor full sum distinguishing total coloring of a graph G is a proper k-total coloring \u03d5 such that no two adjacent vertices u and v satisfy \u03c9(u)\u2260\u03c9(v), where \u03c9(v)=\u03d5(v)+\u2211e\u220bv\u03d5(e)+\u2211u\u2208N(v)\u03d5(u) and N(v)={u|uv\u2208E(G)}. The minimum positive integer k is called the neighbor full sum distinguishing total coloring of G, or ftndi\u03a3(G) for short. In this article, we verify that for a normal planar graph G, ftndi\u03a3(G)\u2264\u0394(G)+3 if g(G)\u22655 and \u0394(G)\u226522, which extends the result of Yue, et al. by reducing the girth condition from 6 to 5.<\/jats:p>","DOI":"10.3390\/axioms14070496","type":"journal-article","created":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T05:53:13Z","timestamp":1750917193000},"page":"496","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Neighbor Full Sum Distinguishing Total Coloring of Planar Graphs with Girth at Least 5"],"prefix":"10.3390","volume":"14","author":[{"given":"Zhongzheng","family":"Yue","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5802-3262","authenticated-orcid":false,"given":"Fei","family":"Wen","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China"},{"name":"Gansu Center for Fundamental Research in Complex Systems Analysis and Control, Lanzhou Jiaotong University, Lanzhou 730070, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1007\/s00373-013-1399-4","article-title":"On the total-neighbor-distinguishing index by sums","volume":"31","year":"2015","journal-title":"Graphs Comb."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.tcs.2015.09.017","article-title":"On the neighbor sum distinguishing total coloring of planar graphs","volume":"609","author":"Qu","year":"2016","journal-title":"Theor. Comput. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.dam.2016.02.003","article-title":"Neighbor sum distinguishing total choosability of planar graphs without 4-cycles","volume":"609","author":"Wang","year":"2016","journal-title":"Discret. Appl. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tcs.2016.11.003","article-title":"Neighbor sum distinguishing total choosability of planar graphs without adjacent triangles","volume":"661","author":"Wang","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.tcs.2017.05.037","article-title":"Neighbor sum distinguishing total coloring of planar graphs without 5-cycles","volume":"689","author":"Ge","year":"2017","journal-title":"Theor. Comput. Sci."},{"key":"ref_6","first-page":"111","article-title":"Neighbor sum distinguishing total choosability of planar graphs without 4-cycles adjacent to 3-cycles","volume":"12","author":"Nakprasit","year":"2022","journal-title":"J. Math. Comput. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"206","DOI":"10.4208\/jms.v56n2.23.06","article-title":"Neighbor Sum Distinguishing Total Chromatic Number of Graphs with Lower Average Degree","volume":"56","author":"Huang","year":"2023","journal-title":"J. Math. Stud."},{"key":"ref_8","first-page":"2350046","article-title":"Neighbor sum distinguishing total coloring of planar graphs with restrained cycles","volume":"16","author":"Du","year":"2024","journal-title":"Discret. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/j.dam.2024.11.005","article-title":"Neighbor sum distinguishing total choosability of planar graphs without intersecting 4-cycles","volume":"361","author":"Duan","year":"2025","journal-title":"Discret. Appl. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"29","DOI":"10.7151\/dmgt.1909","article-title":"A note on neighbor expanded sum distinguishing index","volume":"37","author":"Flandrin","year":"2017","journal-title":"Discuss. Math. Graph Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6959","DOI":"10.3934\/math.2022386","article-title":"Neighbor full sum distinguishing total coloring of Halin graphs","volume":"7","author":"Cheng","year":"2022","journal-title":"AIMS Math."},{"key":"ref_12","first-page":"149","article-title":"Neighbor full sum distinguishing total coloring of graphs","volume":"27","author":"Cui","year":"2023","journal-title":"Oper. Res. Trans."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s11227-024-06825-z","article-title":"Neighbor full sum distinguishing total coloring of planar graphs","volume":"81","author":"Yue","year":"2025","journal-title":"J. Supercomput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1007\/s10878-013-9660-6","article-title":"Neighbor sum distinguishing total colorings of planar graphs","volume":"30","author":"Li","year":"2015","journal-title":"J. Comb. Optim."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/496\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:58:43Z","timestamp":1760032723000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/496"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,25]]},"references-count":14,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["axioms14070496"],"URL":"https:\/\/doi.org\/10.3390\/axioms14070496","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,25]]}}}