en عمومى General پژوهشي Research paper <div style="text-align: justify;">A signed total double Roman k-dominating function (STDRkDF) on an isolated-free graph <em>G = (V, E)</em> is a function <em>f : V (G) &rarr; {-1, 1, 2, 3}</em> such that (i) every vertex <em>v</em> with <em>f(v) = -1</em> has at least two neighbors assigned 2 under<em> f </em>or at least one neighbor <em>w</em> with <em>f(w) = 3</em>, (ii) every vertex <em>v</em> with <em>f(v) = 1</em> has at least one neighbor w with <em>f(w) &ge; 2</em> and (iii) <em>&sum;_u&isin;N(v) f(u) &ge; k</em> holds for any vertex <em>v</em>. The weight of an STDRkDF is the value <em>f(V (G)) = &sum;_{u&isin;V (G)} f(u)</em>. The signed total double Roman <em>k</em>-domination number <em>&gamma;_stdR ^k (G) </em>is the minimum weight among all signed total double Roman <em>k</em>-dominating functions on <em>G</em>. In this paper we present sharp lower bounds for <em>&gamma;_stdR ² (G)</em> and <em>&gamma;_stdR ³ (G)</em> in terms of the order and the size of the graph <em>G</em>.</div> Signed total double Roman k-dominating function, Signed total double Roman k-domination number. 63 77 http://ijmsi.ir/browse.php?a_code=A-10-3392-2&slc_lang=en&sid=1 Laila Shahbazi l.shahbazi@azaruniv.ac.ir 100319475328460011715 100319475328460011715 No Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran Hossein Abdollahzadeh Ahangar ha.ahangar@nit.ac.ir 100319475328460011716 100319475328460011716 Yes Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, I.R. Iran, Postal Code: 47148-71167 Rana Khoeilar khoeilar@azaruniv.ac.ir 100319475328460011717 100319475328460011717 No Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran Seyed Mahmoud Sheikholeslami s.m.sheikholeslami@azaruniv.ac.ir 100319475328460011718 100319475328460011718 No Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran