Title Independent Roman Domination Stable and Vertex-Critical Graphs Type of Research Article Keywords Independent Roman domination, independent Roman stable graph, independent Roman domination vertex critical graphs. Abstract Independent Roman domination, independent Roman stable graph, independent Roman domination vertex critical graphs. Researchers Pu Wu (First Researcher)، Zehui Shao (Second Researcher)، ZHAOHUI WU (Third Researcher)، Zhang Jiang (Fourth Researcher)، Sakineh Nazari-Mogaddam (Fifth Researcher)، Seyed Mahmoud Sheikholeslami Kavkani (Not In First Six Researchers)