An upper bound on triple Roman domination

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Hajjari M.; ABDOLLAHZADEH AHANGAR H.; Khoeilar R.; Shao Z.; SHEIKHOLESLAMI S.M.

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Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2023 | Volume:8 | Issue:3 Page(s): 505-511

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Title

An upper bound on triple Roman domination

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Keywords

triple Roman dominating function

triple Roman domination number

Abstract

For a graph G = (V, E), a triple Roman dominating function (3RD-function) is a function f: V →, {0,1,2,3,4} having the property that (i) if f(v) = 0 then v must have either one neighbor u with f(u) = 4, or two neighbors u, w with f(u) + f(w) ≥,5 or three neighbors u, w,z with f(u) = f(w) = f(z) = 2, (ii) if f(v) = 1 then v must have one neighbor u with f(u) ≥,3 or two neighbors u, w with f(u) = f(w) = 2, and (iii) if f(v) = 2 then v must have one neighbor u with f(u) ≥,2. The weight of a 3RDF f is the sum f(V ) = ∑,v, v f(v), and the minimum weight of a 3RD-function on G is the triple Roman domination number of G, denoted by ɤ,[3R](G). In this paper, we prove that for any connected graph G of order n with minimum degree at least two, ɤ,[3R](G) ≥,3n/2.

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APA: Copy

Hajjari, M., ABDOLLAHZADEH AHANGAR, H., Khoeilar, R., Shao, Z., & SHEIKHOLESLAMI, S.M.. (2023). An upper bound on triple Roman domination. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 8(3), 505-511. SID. https://sid.ir/paper/1057999/en

Vancouver: Copy

Hajjari M., ABDOLLAHZADEH AHANGAR H., Khoeilar R., Shao Z., SHEIKHOLESLAMI S.M.. An upper bound on triple Roman domination. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION[Internet]. 2023;8(3):505-511. Available from: https://sid.ir/paper/1057999/en

IEEE: Copy

M. Hajjari, H. ABDOLLAHZADEH AHANGAR, R. Khoeilar, Z. Shao, and S.M. SHEIKHOLESLAMI, “An upper bound on triple Roman domination,” COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, vol. 8, no. 3, pp. 505–511, 2023, [Online]. Available: https://sid.ir/paper/1057999/en

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