{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T16:38:01Z","timestamp":1756312681671,"version":"3.37.3"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T00:00:00Z","timestamp":1633564800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T00:00:00Z","timestamp":1633564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"University of Bergen"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,12]]},"abstract":"Abstract<\/jats:title>Let $$G=(V,E)$$<\/jats:tex-math>\n \n G<\/mml:mi>\n =<\/mml:mo>\n (<\/mml:mo>\n V<\/mml:mi>\n ,<\/mml:mo>\n E<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> be a graph and $$e=uv\\in E$$<\/jats:tex-math>\n \n e<\/mml:mi>\n =<\/mml:mo>\n u<\/mml:mi>\n v<\/mml:mi>\n \u2208<\/mml:mo>\n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Define $$n_u(e,G)$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n u<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n e<\/mml:mi>\n ,<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> be the number of vertices of G<\/jats:italic> closer to u<\/jats:italic> than to v<\/jats:italic>. The number $$n_v(e,G)$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n v<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n e<\/mml:mi>\n ,<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> can be defined in an analogous way. The Mostar index of G<\/jats:italic> is a new graph invariant defined as $$Mo(G)=\\sum _{uv\\in E(G)}|n_u(uv,G)-n_v(uv,G)|$$<\/jats:tex-math>\n \n M<\/mml:mi>\n o<\/mml:mi>\n \n (<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n =<\/mml:mo>\n \n \u2211<\/mml:mo>\n \n u<\/mml:mi>\n v<\/mml:mi>\n \u2208<\/mml:mo>\n E<\/mml:mi>\n (<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msub>\n \n |<\/mml:mo>\n \n n<\/mml:mi>\n u<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n u<\/mml:mi>\n v<\/mml:mi>\n ,<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n -<\/mml:mo>\n \n n<\/mml:mi>\n v<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n u<\/mml:mi>\n v<\/mml:mi>\n ,<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n |<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The edge version of Mostar index is defined as $$Mo_e(G)=\\sum _{e=uv\\in E(G)} |m_u(e|G)-m_v(G|e)|$$<\/jats:tex-math>\n \n M<\/mml:mi>\n \n o<\/mml:mi>\n e<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n =<\/mml:mo>\n \n \u2211<\/mml:mo>\n \n e<\/mml:mi>\n =<\/mml:mo>\n u<\/mml:mi>\n v<\/mml:mi>\n \u2208<\/mml:mo>\n E<\/mml:mi>\n (<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msub>\n \n |<\/mml:mo>\n \n m<\/mml:mi>\n u<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n e<\/mml:mi>\n |<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n -<\/mml:mo>\n \n m<\/mml:mi>\n v<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n G<\/mml:mi>\n |<\/mml:mo>\n e<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n |<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where $$m_u(e|G)$$<\/jats:tex-math>\n \n \n m<\/mml:mi>\n u<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n e<\/mml:mi>\n |<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$m_v(e|G)$$<\/jats:tex-math>\n \n \n m<\/mml:mi>\n v<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n e<\/mml:mi>\n |<\/mml:mo>\n G<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are the number of edges of G<\/jats:italic> lying closer to vertex u<\/jats:italic> than to vertex v<\/jats:italic> and the number of edges of G<\/jats:italic> lying closer to vertex v<\/jats:italic> than to vertex u<\/jats:italic>, respectively. Let G<\/jats:italic> be a connected graph constructed from pairwise disjoint connected graphs $$G_1,\\ldots ,G_k$$<\/jats:tex-math>\n \n \n G<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \u2026<\/mml:mo>\n ,<\/mml:mo>\n \n G<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> by selecting a vertex of $$G_1$$<\/jats:tex-math>\n \n G<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a vertex of $$G_2$$<\/jats:tex-math>\n \n G<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and identifying these two vertices. Then continue in this manner inductively. We say that G<\/jats:italic> is a polymer graph, obtained by point-attaching from monomer units $$G_1,\\ldots ,G_k$$<\/jats:tex-math>\n \n \n G<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n ,<\/mml:mo>\n \u2026<\/mml:mo>\n ,<\/mml:mo>\n \n G<\/mml:mi>\n k<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In this paper, we consider some particular cases of these graphs that are of importance in chemistry and study their Mostar and edge Mostar indices.<\/jats:p>","DOI":"10.1007\/s40314-021-01652-x","type":"journal-article","created":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T09:39:12Z","timestamp":1633599552000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Mostar index and edge Mostar index of polymers"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5063-3461","authenticated-orcid":false,"given":"Nima","family":"Ghanbari","sequence":"first","affiliation":[]},{"given":"Saeid","family":"Alikhani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,7]]},"reference":[{"key":"1652_CR1","doi-asserted-by":"crossref","unstructured":"Akhter SH, Iqbal Z, Aslam A, Gao W (2021) Computation of Mostar index for some graph operations. 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