>
Fa   |   Ar   |   En
   weak signed roman k-domatic number of a graph  
   
Ω†ΩˆΫŒΨ³Ω†Ψ―Ω‡ volkmann lutz
Ω…Ω†Ψ¨ΨΉ communications in combinatorics and optimization - 2022 - Ψ―ΩˆΨ±Ω‡ : 7 - Ψ΄Ω…Ψ§Ψ±Ω‡ : 1 - ءفحه:17 -27
Ϊ†Ϊ©ΫŒΨ―Ω‡    Let π‘˜β‹1 be an integer. a weak signed roman π‘˜-dominating function} on a graph 𝐺 isa function Β  Ζ’:𝑉 (𝐺)β†’ {-1, 1, 2} such that βˆ‘π‘’ Ο΅ 𝑁 [𝑣] Ζ’(𝑒)β‹π‘˜ for every 𝑣 ϡ𝑉(𝐺) , where 𝑁 [𝑣] is the closed neighborhood of v .a set {Ζ’1,Ζ’2,....,ƒ𝑑} of distinct weak signed roman π‘˜-dominatingfunctions on 𝐺 with the property that βˆ‘π‘‘π‘–=1 ƒ𝑖(𝑣)β‹œ π‘˜ for each 𝑣 Ο΅ 𝑉(𝐺) , is called a weak signed roman π‘˜-dominating family of functions on 𝐺. the maximum number of functionsin a Β weak signed roman π‘˜-dominating family on 𝐺 is the weak signed roman π‘˜-domatic number} of 𝐺, denoted by π‘‘π‘˜Ο‰π‘ π‘…(𝐺). in this paper we initiate the study of the weak signed roman π‘˜-domatic numberin graphs, and we present sharp bounds for π‘‘π‘˜Ο‰π‘ π‘…(𝐺) . in addition, we determine the weak signed romanπ‘˜-domatic number of some graphs.
Ϊ©Ω„ΫŒΨ―ΩˆΨ§Ϊ˜Ω‡ weak signed roman π‘˜-dominating function ,weak signed roman π‘˜-domination number ,weak signed roman k-domatic number
Ψ’Ψ―Ψ±Ψ³ rwth aachen university, lehrstuhl ii fur mathematik, germany
ΩΎΨ³Ψͺ Ψ§Ω„Ϊ©ΨͺΨ±ΩˆΩ†ΫŒΪ©ΫŒ volkm@math2.rwth-aachen.de
 
     
   
Authors
  
 
 

Copyright 2023
Islamic World Science Citation Center
All Rights Reserved