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In this paper, we solve some problems posed by Vuki\u010devi\u0107 &lt;sup&gt;[&lt;xref ref-type=\"bibr\" rid=\"b1\"&gt;1&lt;\/xref&gt;]&lt;\/sup&gt;, and we characterize graphs with maximum and minimum values of the $ IS\\!D_a $ index, for $ a &amp;lt; 0 $, in the following sets of graphs with $ n $ vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2023387","type":"journal-article","created":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T12:47:41Z","timestamp":1678366061000},"page":"8800-8813","source":"Crossref","is-referenced-by-count":1,"title":["On the variable inverse sum deg index"],"prefix":"10.3934","volume":"20","author":[{"given":"Edil D.","family":"Molina","sequence":"first","affiliation":[{"name":"Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Guerrero, Carlos E. Adame No.54 Col. 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