{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:07:04Z","timestamp":1768010824087,"version":"3.49.0"},"reference-count":0,"publisher":"Combinatorial Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>An outer independent double Roman dominating function (OIDRDF) on a graph  G  is a function  f : V ( G ) \u2192 { 0 , 1 , 2 , 3 }  having the property that (i) if  f ( v ) = 0 , then the vertex  v  must have at least two neighbors assigned 2 under  f  or one neighbor  w  with  f ( w ) = 3 , and if  f ( v ) = 1 , then the vertex  v  must have at least one neighbor  w  with  f ( w ) \u2265 2  and (ii) the subgraph induced by the vertices assigned 0 under  f  is edgeless. The weight of an OIDRDF is the sum of its function values over all vertices, and the outer independent double Roman domination number  \u03b3 o i d R ( G )  is the minimum weight of an OIDRDF on  G . The  \u03b3 o i d R -stability ( \u03b3 \u2212 o i d R -stability,  \u03b3 + o i d R -stability) of  G , denoted by  s t \u03b3 o i d R ( G )  ( s t \u2212 \u03b3 o i d R ( G ) ,  s t + \u03b3 o i d R ( G ) ), is defined as the minimum size of a set of vertices whose removal changes (decreases, increases) the outer independent double Roman domination number. In this paper, we determine the exact values on the  \u03b3 o i d R -stability of some special classes of graphs, and present some bounds on  s t \u03b3 o i d R ( G ) . In addition, for a tree  T  with maximum degree  \u0394 , we show that  s t \u03b3 o i d R ( T ) = 1  and  s t \u2212 \u03b3 o i d R ( T ) \u2264 \u0394 , and characterize the trees that achieve the upper bound.<\/jats:p>","DOI":"10.61091\/ars-160-04","type":"journal-article","created":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T21:36:01Z","timestamp":1728250561000},"page":"21-29","source":"Crossref","is-referenced-by-count":2,"title":["Outer Independent Double Roman Domination Stability in Graphs"],"prefix":"10.61091","volume":"160","author":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.M.","family":"Sheikholeslami","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Esmaeili","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Volkmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Lehrstuhl II fur Mathematik RWTH Aachen University 52056 Aachen, Germany","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2024,9,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T21:36:05Z","timestamp":1728250565000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-160\/outer-independent-double-roman-domination-stability-in-graphs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,9,30]]},"published-print":{"date-parts":[[2024,9,30]]}},"URL":"https:\/\/doi.org\/10.61091\/ars-160-04","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,30]]}}}