Nordhaus-Gaddum type inequalities on the total Italian domination number in graphs

被引:3
作者
Sheikholeslami, Seyed Mahmoud [1 ]
Volkmann, Lutz [2 ]
机构
[1] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran
[2] Rhein Westfal TH Aachen, Lehrstuhl II Math, D-52056 Aachen, Germany
关键词
Total domination; total Italian domination number; total Roman domination; TOTAL ROMAN DOMINATION; TRANSVERSALS;
D O I
10.1051/ro/2022108
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
Let G be a graph with vertex set V(G). A total Italian dominating function (TIDF) on a graph G is a function f : V(G) -> {0, 1, 2} such that (i) every vertex v with f(v) = 0 is adjacent to a vertex u with f(u) = 2 or to two vertices w and z with f(w) = f(z) = 1, and (ii) every vertex v with f(v) >= 1 is adjacent to a vertex u with f(u) >= 1. The total Italian domination number gamma(tI)(G) on a graph G is the minimum weight of a total Italian dominating function. In this paper, we present Nordhaus-Gaddum type inequalities for the total Italian domination number.
引用
收藏
页码:2235 / 2243
页数:9
相关论文
共 21 条
[1]  
Ahangar HA, 2022, B IRAN MATH SOC, V48, P1111, DOI 10.1007/s41980-021-00565-z
[2]   Total Roman {2}-Dominating Functions in Graphs [J].
Ahangar, H. Abdollahzadeh ;
Chellali, M. ;
Sheikholeslami, S. M. ;
Valenzuela-Tripodoro, J. C. .
DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2022, 42 (03) :937-958
[3]   TOTAL ROMAN DOMINATION IN GRAPHS [J].
Ahangar, Hossein Abdollahzadeh ;
Henning, Michael A. ;
Samodivkin, Vladimir ;
Yero, Ismael G. .
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2016, 10 (02) :501-517
[4]   Nordhaus-Gaddum bounds for total Roman domination [J].
Amjadi, J. ;
Sheikholeslami, S. M. ;
Soroudi, M. .
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2018, 35 (01) :126-133
[5]   Total Roman domination subdivision number in graphs [J].
Amjadi, Jafar .
COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2020, 5 (02) :157-168
[6]   ON THE TOTAL ROMAN DOMINATION IN TREES [J].
Amjadi, Jafar ;
Sheikholeslami, Seyed Mahmoud ;
Soroudi, Marzieh .
DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2019, 39 (02) :519-532
[7]  
[Anonymous], 1998, FUNDAMENTALS DOMINAT, DOI 10.1201/9781482246582
[8]   Total Roman {2}-domination in graphs [J].
Cabrera Garcia, Suitberto ;
Cabrera Martinez, Abel ;
Hernandez Mira, Frank A. ;
Yero, Ismael G. .
QUAESTIONES MATHEMATICAE, 2021, 44 (03) :411-434
[9]   A characterization relating domination, semitotal domination and total Roman domination in trees [J].
Cabrera Martinez, Abel ;
Martinez Arias, Alondra ;
Menendez Castillo, Maikel .
COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2021, 6 (02) :197-209
[10]   Algorithmic aspects of total Roman {2}-domination in graphs [J].
Chakradhar, P. ;
Reddy, P. Venkata Subba .
COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2022, 7 (02) :183-192