{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:28:42Z","timestamp":1740148122034,"version":"3.37.3"},"reference-count":39,"publisher":"Wiley","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational Intelligence and Neuroscience"],"published-print":{"date-parts":[[2017]]},"abstract":"A signed graph<\/jats:italic> is a simple graph where each edge receives a sign positive or negative. Such graphs are mainly used in social sciences where individuals represent vertices friendly relation between them as a positive edge and enmity as a negative edge. In signed graphs, we define these relationships (edges) as of friendship (\u201c+<\/mml:mo><\/mml:mrow><\/mml:math>\u201d edge) or hostility (\u201c-<\/mml:mo><\/mml:mrow><\/mml:math>\u201d edge). A 2-path product signed graph <\/jats:italic>S<\/mml:mi>#<\/mml:mo><\/mml:mrow>^<\/mml:mo><\/mml:mover>S<\/mml:mi><\/mml:math> of a signed graph S<\/mml:mi><\/mml:mrow><\/mml:math> is defined as follows: the vertex set is the same as S<\/mml:mi><\/mml:mrow><\/mml:math> and two vertices are adjacent if and only if there exists a path of length two between them in S<\/mml:mi><\/mml:mrow><\/mml:math>. The sign of an edge is the product of marks of vertices in S<\/mml:mi><\/mml:mrow><\/mml:math> where the mark of vertex u<\/mml:mi><\/mml:mrow><\/mml:math> in S<\/mml:mi><\/mml:mrow><\/mml:math> is the product of signs of all edges incident to the vertex. In this paper, we give a characterization of 2-path product signed graphs. Also, some other properties such as sign-compatibility and canonically-sign-compatibility of 2-path product signed graphs are discussed along with isomorphism and switching equivalence of this signed graph with 2-path signed graph.<\/jats:p>","DOI":"10.1155\/2017\/1235715","type":"journal-article","created":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T17:05:33Z","timestamp":1499360733000},"page":"1-8","source":"Crossref","is-referenced-by-count":2,"title":["Characterization of 2-Path Product Signed Graphs with Its Properties"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5695-5282","authenticated-orcid":true,"given":"Deepa","family":"Sinha","sequence":"first","affiliation":[{"name":"Department of Mathematics, South Asian University, Akbar Bhawan Chanakyapuri, New Delhi 110021, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deepakshi","family":"Sharma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Asian University, Akbar Bhawan Chanakyapuri, New Delhi 110021, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/00223980.1946.9917275"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1037\/h0046049"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-015-1666-7"},{"issue":"2","key":"5","first-page":"189","volume":"6","year":"2013","journal-title":"European Journal of Pure and Applied Mathematics"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-013-0767-z"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2015.2401014"},{"year":"2010","key":"10"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s40009-015-0373-5"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.10.026"},{"issue":"2","key":"13","first-page":"115","volume":"3","year":"2006","journal-title":"AKCE International Journal of Graphs and Combinatorics"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.22342\/jims.16.2.34.105-113"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1023\/B:CMAJ.0000042369.18091.15"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-005-0002-4"},{"key":"17","first-page":"49","volume":"24","year":"1969","journal-title":"Elemente der Mathematik"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-015-0962-8"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(82)90033-6"},{"issue":"3","key":"20","first-page":"389","volume":"36","year":"2012","journal-title":"Southeast Asian Bulletin of Mathematics"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.5614\/ejgta.2014.2.1.3"},{"key":"22","first-page":"74","volume":"1","year":"2015","journal-title":"Mathematical Combinatorics"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265915500115"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.3233\/FI-2016-1345"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.3233\/FI-2016-1377"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.3233\/FI-2016-1378"},{"year":"1969","key":"29"},{"year":"2001","key":"30"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(96)00386-X"},{"volume":"1000:ds8","journal-title":"Electronic Journal of Combinatorics","year":"2012","key":"32"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.1145\/362342.362367"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1016\/0165-4896(80)90010-4"},{"issue":"4","key":"33","first-page":"14","volume":"11","year":"2012","journal-title":"Mapana-Journal of Sciences"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1002\/bs.3830030102"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90090-7"},{"issue":"6","key":"36","first-page":"567","volume":"15","year":"1981","journal-title":"Journal of Mathematical and Physical Sciences"},{"issue":"16","key":"38","first-page":"1","volume":"4","year":"2009","journal-title":"Notes on Number Theory and Discrete Mathematics"},{"issue":"3","key":"39","first-page":"91","volume":"7","year":"1984","journal-title":"National Academy Science Letters"},{"journal-title":"Social networks. 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