مشخصات پژوهش

A signed total double Roman dominating function (STDRD-function) on an isolated-free graph G is a function f VG : ( ) { 1,1,2,3} satisfying the conditions (i) f Nv ( ( ))= f z( ) 1 z Nv( ) for every vertex v VG( ) and (ii) if f v( )= 1, then the vertex vmust have a neighbor assigned 3 or two neighbors assigned 2 under f, and if f v( )=1, then v must have at least one neighbor assigned at least 2. The weight of an STDRD-function f is the value f VG f x ( ( ))= ( ) x VG( ) , and the signed total double Roman domination number (or simply STDRD-number) G( ) sdR t of Gis the minimum weight of an STDRD-function of G. In this work, we establish several new bounds for the STDRD-number, which refine and extend previously known results. Moreover, we provide an exact determination of the STDRD-number in the case of perfect binary trees.