A Roman dominating function on a graph G = (V, E) is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V) = ∑u∈V(G)f(u). The minimum possible weight of a Roman dominating function on G is called the Roman domination number of G and is denoted by γR(G). In this paper, and among some other results, we provide some bounds for the Roman domination number of the subdivision graph S(G) of an arbitrary graph G. Also, we determine the exact value of γR(S(G)) when G is Kn, Kr,s or Kn1,n2,...,nk .
Yarke Salkhori, R., Vatandoost, E., & Behtoei, A. (2024). On the Roman domination number of the subdivision of some graphs. Journal of Discrete Mathematics and Its Applications, 9(4), 321-333. doi: 10.22061/jdma.2024.11309.1099
MLA
Rostam Yarke Salkhori; Ebrahim Vatandoost; Ali Behtoei. "On the Roman domination number of the subdivision of some graphs", Journal of Discrete Mathematics and Its Applications, 9, 4, 2024, 321-333. doi: 10.22061/jdma.2024.11309.1099
HARVARD
Yarke Salkhori, R., Vatandoost, E., Behtoei, A. (2024). 'On the Roman domination number of the subdivision of some graphs', Journal of Discrete Mathematics and Its Applications, 9(4), pp. 321-333. doi: 10.22061/jdma.2024.11309.1099
VANCOUVER
Yarke Salkhori, R., Vatandoost, E., Behtoei, A. On the Roman domination number of the subdivision of some graphs. Journal of Discrete Mathematics and Its Applications, 2024; 9(4): 321-333. doi: 10.22061/jdma.2024.11309.1099
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