Quasi-total Roman bondage number in graphs by Huiqin Jiang, Zehui Shao

“…We first show that the decision problem associated with the quasi-total Roman bondage problem is NP-hard even when restricted to bipartite graphs. Then basic properties of the quasi-total Roman bondage number are provided. …”
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Independent Roman Domination: The Complexity and Linear-Time Algorithm for Trees by Zhixing Duan, Huiqin Jiang, Xinyue Liu, Pu Wu, Zehui Shao

“…In this paper, we prove that the decision problem of minimum IRDF is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>P</mi></mrow></semantics></math></inline-formula>-complete for chordal bipartite graphs. Then, we research the difference in complexity between the decision problem of RDF and IRDF. …”
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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees by Xinyue Liu, Huiqin Jiang, Pu Wu, Zehui Shao

“…In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>t</mi><mo stretchy="false">{</mo><mi>R</mi><mn>3</mn><mo stretchy="false">}</mo></mrow></msub></semantics></math></inline-formula> for trees.…”
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Total Roman {3}-domination in Graphs by Zehui Shao, Doost Ali Mojdeh, Lutz Volkmann

“…Finally, we investigate the complexity of total Roman <inline-formula> <math display="inline"> <semantics> <mrow> <mo>{</mo> <mn>3</mn> <mo>}</mo> </mrow> </semantics> </math> </inline-formula>-domination for bipartite graphs.…”
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