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The minimum degree and isolated toughness characterize network topology from the perspectives of sparsity and stability, which serves as the theoretical conditions for fractional factors. This article reveals from a theoretical perspective that if the minimum degree condition increases, the corresponding tight isolated toughness variant bound will decrease. This infinite number of parameter combinations cause a \u201cchoice dilemma\u201d for decision-makers. To solve this problem, we regard these two parameters as the Pareto front of the bi-objective optimization problem, and a knot point calculation approach is designed to determine the optimal combination.<\/jats:p>","DOI":"10.1051\/ita\/2025017","type":"journal-article","created":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T08:51:43Z","timestamp":1763542303000},"page":"19","source":"Crossref","is-referenced-by-count":0,"title":["Decision making strategy for \u03b4 \u2212\n                    <i>I<\/i>\n                    equilibrium problem in network designing"],"prefix":"10.1051","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4718-5677","authenticated-orcid":false,"given":"Yaojun","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Minnan Normal University","place":["PR China"]}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3185-2748","authenticated-orcid":false,"given":"Hainan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Software Engineering, South China University of Technology","place":["PR China"]}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7856-9828","authenticated-orcid":false,"given":"Wei","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hohai University","place":["PR China"]}]}],"member":"250","published-online":{"date-parts":[[2025,11,19]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Bondy J.A. and Mutry U.S.R., Graph Theory. 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