{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:44Z","timestamp":1777704344541,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,7,16]],"date-time":"2018-07-16T00:00:00Z","timestamp":1531699200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,10,27]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>G<\/jats:italic>\n                    = (\n                    <jats:italic>V<\/jats:italic>\n                    ,\n                    <jats:italic>E<\/jats:italic>\n                    ) be a connected graph. An edge set\n                    <jats:italic>S<\/jats:italic>\n                    \u2282\n                    <jats:italic>E<\/jats:italic>\n                    is a 3-restricted edge cut, if\n                    <jats:italic>G<\/jats:italic>\n                    -\n                    <jats:italic>S<\/jats:italic>\n                    is disconnected and every component of\n                    <jats:italic>G<\/jats:italic>\n                    -\n                    <jats:italic>S<\/jats:italic>\n                    has at least three vertices. The 3-restricted edge connectivity\n                    <jats:italic>\u03bb<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    (\n                    <jats:italic>G<\/jats:italic>\n                    ) of\n                    <jats:italic>G<\/jats:italic>\n                    is the cardinality of a minimum restricted edge cut of\n                    <jats:italic>G<\/jats:italic>\n                    . A graph\n                    <jats:italic>G<\/jats:italic>\n                    is\n                    <jats:italic>\u03bb<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    -connected, if 3-restricted edge cuts exist. A graph\n                    <jats:italic>G<\/jats:italic>\n                    is called\n                    <jats:italic>\u03bb<\/jats:italic>\n                    \u2032-optimal, if\n                    <jats:italic>\u03bb<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    (\n                    <jats:italic>G<\/jats:italic>\n                    ) =\n                    <jats:italic>\u03be<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    (\n                    <jats:italic>G<\/jats:italic>\n                    ), where\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi>\u03be<\/mml:mi>\n                          <mml:mn>3<\/mml:mn>\n                        <\/mml:msub>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>G<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mo>min<\/mml:mo>\n                        <mml:mo>{<\/mml:mo>\n                        <mml:mo>|<\/mml:mo>\n                        <mml:mo>[<\/mml:mo>\n                        <mml:mi>X<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mover accent=\"true\">\n                          <mml:mi>X<\/mml:mi>\n                          <mml:mo>\u00af<\/mml:mo>\n                        <\/mml:mover>\n                        <mml:mo>]<\/mml:mo>\n                        <mml:mo>|<\/mml:mo>\n                        <mml:mo>:<\/mml:mo>\n                        <mml:mi>X<\/mml:mi>\n                        <mml:mo>\u2282<\/mml:mo>\n                        <mml:mi>V<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mo>|<\/mml:mo>\n                        <mml:mi>X<\/mml:mi>\n                        <mml:mo>|<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:mn>3<\/mml:mn>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mi>G<\/mml:mi>\n                        <mml:mo>[<\/mml:mo>\n                        <mml:mi>X<\/mml:mi>\n                        <mml:mo>]<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    is connected}. Furthermore, if every minimum 3-restricted edge cut is a set of edges incident to a set of three vertices, then G is said to be super 3-restricted edge connected or super-\n                    <jats:italic>\u03bb<\/jats:italic>\n                    <jats:sub>3<\/jats:sub>\n                    for simplicity. Inverse degree of\n                    <jats:italic>G<\/jats:italic>\n                    is\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>R<\/mml:mi>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>G<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                        <mml:mo>=<\/mml:mo>\n                        <mml:msub>\n                          <mml:mo>\u2211<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mi>v<\/mml:mi>\n                            <mml:mo>\u2208<\/mml:mo>\n                            <mml:mi>V<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mrow>\n                          <mml:mfrac>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mrow>\n                              <mml:mi>d<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>v<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mfrac>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:italic>d<\/jats:italic>\n                    (\n                    <jats:italic>v<\/jats:italic>\n                    ) denotes the degree of the vertex\n                    <jats:italic>v<\/jats:italic>\n                    . In this paper, we study the relation of inverse degree and super 3-restricted edge connected graphs.\n                  <\/jats:p>","DOI":"10.3233\/jifs-169718","type":"journal-article","created":{"date-parts":[[2018,7,17]],"date-time":"2018-07-17T12:13:59Z","timestamp":1531829639000},"page":"3955-3958","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Restricted edge connectivity of graphs on degree"],"prefix":"10.1177","volume":"35","author":[{"given":"Litao","family":"Guo","sequence":"first","affiliation":[{"name":"School of Applied Mathematics, Xiamen University of Technology, Xiamen Fujian, People\u2019s Republic of China"}]},{"given":"Bernard L.S.","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Science, Jimei University, Xiamen, People\u2019s Republic of China"}]}],"member":"179","published-online":{"date-parts":[[2018,7,16]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/09720502.2016.1188468"},{"issue":"1","key":"e_1_3_1_3_2","first-page":"108","article-title":"Genetic variability among seven cultivars of date palm (Phoenix dactylifera L.) based on embryonic DNA of old fruit","volume":"45","author":"Aladadi W.M.","year":"2018","unstructured":"AladadiW.M., MoustafaM.F. and AlrumanS.A., Genetic variability among seven cultivars of date palm (Phoenix dactylifera L.) based on embryonic DNA of old fruit, Kuwait Journal of Science45(1) (2018), 108\u2013114.","journal-title":"Kuwait Journal of Science"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/09720529.2016.1178930"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)00369-T"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2016.1197214"},{"issue":"7","key":"e_1_3_1_7_2","first-page":"3227","article-title":"A study of investigating adolescents\u2019 eating out behavior by using analytic hierarchy process","volume":"13","author":"Lan T.","year":"2017","unstructured":"LanT., LanY., ChenP. and LoW., A study of investigating adolescents\u2019 eating out behavior by using analytic hierarchy process, Eurasia Journal of Mathematics Science and Technology Education13(7) (2017), 3227\u20133234.","journal-title":"Eurasia Journal of Mathematics Science and Technology Education"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sjbs.2015.10.027"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.06.035"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00385-0"},{"key":"e_1_3_1_11_2","first-page":"23","article-title":"On conjectures of Graffiti \u2013 III","volume":"66","author":"Fajtlowicz S.","year":"1988","unstructured":"FajtlowiczS., On conjectures of Graffiti \u2013 III, Congressus Numerantium66 (1988), 23\u201332.","journal-title":"Congressus Numerantium"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.07.053"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.06.041"},{"key":"e_1_3_1_14_2","unstructured":"BondyJ.A. and MurtyU.S.R. 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