{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T07:31:27Z","timestamp":1779003087791,"version":"3.51.4"},"reference-count":14,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T00:00:00Z","timestamp":1625702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity \u03ba(G)\u2264\u03ba\u2032(G)\u2264\u03b4(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3\u20135.<\/jats:p>","DOI":"10.3390\/sym13071227","type":"journal-article","created":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T10:42:17Z","timestamp":1625740937000},"page":"1227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Connectivity of Semiring Valued Graphs"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9740-3081","authenticated-orcid":false,"given":"Shyam Sundar","family":"Santra","sequence":"first","affiliation":[{"name":"Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prabhakaran","family":"Victor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641021, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahadevan","family":"Chandramouleeswaran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Ramanas College of Arts and Science for Women, Aruppukottai 626134, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rami Ahmad","family":"El-Nabulsi","sequence":"additional","affiliation":[{"name":"Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Athens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4167-1690","authenticated-orcid":false,"given":"Khaled Mohamed","family":"Khedher","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia"},{"name":"Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vediyappan","family":"Govindan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dmi St John The Baptist University, Mangochi P.O. Box 406, Malawi"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Godsil, C., and Royle, G. (2001). Algebraic Graph Theory, Springer.","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"ref_2","first-page":"141","article-title":"Semiring Valued Graphs","volume":"9","author":"Rajkumar","year":"2015","journal-title":"Int. J. Math. Sci. Engg. Appls."},{"key":"ref_3","first-page":"2971","article-title":"Regularity on S- valued graphs","volume":"2","author":"Jeyalakshmi","year":"2015","journal-title":"Glob. J. Pure Appl. Math"},{"key":"ref_4","first-page":"323","article-title":"Connected S-Valued Graphs","volume":"4","author":"Jeyalakshmi","year":"2015","journal-title":"Math. Sci. Int. Res. J."},{"key":"ref_5","first-page":"326","article-title":"Degree regular S-valued graphs","volume":"4","author":"Rajkumar","year":"2015","journal-title":"Math. Sci. Int. J. Math. Sci. Eng. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Beineke, L.W., and Wilson, R.J. (2004). Topics in Algebraic Graph Theory, Cambridge University Press.","DOI":"10.1017\/CBO9780511529993"},{"key":"ref_7","unstructured":"Biggs, N. (1993). Algebraic Graph Theory, Cambridge University Press."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/BF01210984","article-title":"Graph derivations","volume":"76","author":"Sabidussi","year":"1961","journal-title":"Math. 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Semirings and Their Applications, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-017-0383-3_1"},{"key":"ref_14","first-page":"121","article-title":"Diameter on S-valued Graphs","volume":"6","author":"Jeyalakshmi","year":"2017","journal-title":"Math. Sci. Int. Res. J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1227\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:27:49Z","timestamp":1760164069000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/7\/1227"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,8]]},"references-count":14,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["sym13071227"],"URL":"https:\/\/doi.org\/10.3390\/sym13071227","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,8]]}}}