부산대학교 도서관

"A function f : V (G) → {0, 1, 2, 3} such that every vertex v with f (v)= 0 has at least two neighbors with label 2 or one neighbor with label 3 and every vertex v with f (v)= 1 has at least one neighbor with label 2 or 3 is called a double Roman dominating function (DRDF) of G. This function's weight is denoted by w(f) which is the sum of the labelings of the vertices. If f is a DRDF of minimum weight, then its inverse double Roman dominating function (IDRDF) f' is also a DRDF on G, such that fʹ (v)= 0, ∀ v ∈ S where S = {v ∈ V/ f (v) > 0}. The minimum weight of such a function is the inverse double Roman domination number (IDRDN) of G and is denoted by γidR (G). "We define different criticality concepts for γidR (G). We also characterize the vertex/edge critical graphs and vertex/edge super critical graphs. [ABSTRACT FROM AUTHOR]