فهرست نشریات علمی دسترسی آزاد ایران

‎‎A vertex $v$ in a graph $G$ is said to be over-dominated by a subset $S$ of vertices of $G$ if $|N[v]\cap S|\geq 2$‎. ‎The cardinality--redundance of $S$‎, ‎which we denote by $CR(S)$‎, ‎is the number of vertices of $G$ that are over-dominated by $S$‎. ‎The cardinality--redundance number of a graph $G$‎, ‎which we denote by $CR(G)$‎, ‎is the minimum among all cardinality--redundances $CR(S)$ taken over all dominating sets $S$‎. ‎In this paper‎, ‎we study those graphs whose cardinality--redundance decreases by two upon the removal of any arbitrary edge‎. ‎We refer to such graphs as cardinality--redundance strong edge critical graphs‎. ‎We give a general characterization for all cardinality--redundance strong edge critical graphs‎, ‎and then focus on the cardinality--redundance strong edge critical graphs having cardinality--redundance $2$‎, ‎and present several characterizations for these graphs‎.