Unique response strong Roman dominating functions of graphs
Given a simple graph G=(V,E) with maximum degree Δ. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ∈ V : f(v)=i} for i = 0, 1 and V2 = {v ∈ V : f(v)≥2}. A function f : V → {0, 1, ..., ⌈Δ/2⌉+1} is a strong Roman dominating function (StRDF) on G, if every v ∈ V0 has a neighbor w ∈ V2 and...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2021-10-16.
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| LEADER | 02970 am a22002893u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_981_pdf_193 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Mojdeh, Doost Ali; Department of Mathematics, University of Mazandaran, Babolsar, Iran |e author |
| 100 | 1 | 0 | |a National Natural Science Foundation of China |e contributor |
| 700 | 1 | 0 | |a Hao, Guoliang; College of Science, East China University of Technology, Nanchang 330013, People's Republic of China |e author |
| 700 | 1 | 0 | |a Masoumi, Iman; Department of Mathematics, University of Tafresh, Tafresh, Iran |e author |
| 700 | 1 | 0 | |a Parsian, Ali; Department of Mathematics, University of Tafresh, Tafresh, Iran |e author |
| 245 | 0 | 0 | |a Unique response strong Roman dominating functions of graphs |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2021-10-16. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/981 | ||
| 520 | |a Given a simple graph G=(V,E) with maximum degree Δ. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ∈ V : f(v)=i} for i = 0, 1 and V2 = {v ∈ V : f(v)≥2}. A function f : V → {0, 1, ..., ⌈Δ/2⌉+1} is a strong Roman dominating function (StRDF) on G, if every v ∈ V0 has a neighbor w ∈ V2 and f(w)≥1 + ⌈1/2|N(w)∩V0|⌉. A function f : V → {0, 1, ..., ⌈Δ/2⌉+1} is a unique response strong Roman function (URStRF), if w ∈ V0, then |N(w)∩V2|≤1 and w ∈ V1 ∪ V2 implies that |N(w)∩V2|=0. A function f : V → {0, 1, ..., ⌈Δ/2⌉+1} is a unique response strong Roman dominating function (URStRDF) if it is both URStRF and StRDF. The unique response strong Roman domination number of G, denoted by uStR(G), is the minimum weight of a unique response strong Roman dominating function. In this paper we approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, for any tree T of order n ≥ 3 we prove the sharp bound uStR(T)≤8n/9. | ||
| 540 | |a Copyright (c) 2021 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a strong Roman dominating function, unique response strong Roman (dominating) function | ||
| 690 | |a 05C69 | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications; 469 - 484 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/981/pdf_193 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/981/pdf_193 |z Get Fulltext |