{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:12Z","timestamp":1760242812158,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,12,2]],"date-time":"2016-12-02T00:00:00Z","timestamp":1480636800000},"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>A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery     P ( G )     is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if     e ( v ) = r a d ( G )    , and the subgraph of G induced by its central vertices is called center     C ( G )     of     G .     Average eccentricity is the sum of eccentricities of all of the vertices in a graph divided by the total number of vertices, i.e.,     a v e c  ( G )  = {  1 n  \u2211  e G   ( u )  ;     u \u2208 V ( G )  } .     If every vertex in G is central vertex, then     C ( G ) = G    , and hence, G is self-centered. In this report, we find the center, periphery and average eccentricity for the convex polytopes.<\/jats:p>","DOI":"10.3390\/sym8120145","type":"journal-article","created":{"date-parts":[[2016,12,2]],"date-time":"2016-12-02T10:36:37Z","timestamp":1480674997000},"page":"145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On Center, Periphery and Average Eccentricity for the Convex Polytopes"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5488-0467","authenticated-orcid":false,"given":"Waqas","family":"Nazeer","sequence":"first","affiliation":[{"name":"Division of Science and Technology, University of Education, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea"},{"name":"Center for General Education, China Medical University, Taichung 40402, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saima","family":"Nazeer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mobeen","family":"Munir","sequence":"additional","affiliation":[{"name":"Division of Science and Technology, University of Education, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Imrana","family":"Kousar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ammara","family":"Sehar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young","family":"Kwun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dong-A University, Busan 49315, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,2]]},"reference":[{"key":"ref_1","first-page":"611","article-title":"On Connective Eccentricity Index of Graphs","volume":"69","author":"Yu","year":"2013","journal-title":"MATCH Commun. 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