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A note on independent domination in almost-regular graphs.

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Τίτλος: A note on independent domination in almost-regular graphs.
Συγγραφείς: Goddard, Wayne1,2 goddard@clemson.edu, Henning, Michael A.2 mahenning@uj.ac.za
Πηγή: Communications in Combinatorics & Optimization. Dec2026, Vol. 11 Issue 4, p1175-1180. 6p.
Θεματικοί όροι: *Regular graphs, *Dominating set, *Bipartite graphs, *Graph theory
Περίληψη: A classic result in domination theory is that a regular graph has in- dependent domination number at most half the order. We strengthen this result to \almost-regular" graphs by showing that if a graph has minimum degree d > 0 and maximum degree at most d + 3, and the subgraph induced by the vertices of degree d +3 (if any) is bipartite, then the independent domination number is at most half the order. We also discuss related questions. [ABSTRACT FROM AUTHOR]
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  Data: A note on independent domination in almost-regular graphs.
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  Data: <searchLink fieldCode="AR" term="%22Goddard%2C+Wayne%22">Goddard, Wayne</searchLink><relatesTo>1,2</relatesTo><i> goddard@clemson.edu</i><br /><searchLink fieldCode="AR" term="%22Henning%2C+Michael+A%2E%22">Henning, Michael A.</searchLink><relatesTo>2</relatesTo><i> mahenning@uj.ac.za</i>
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  Data: <searchLink fieldCode="JN" term="%22Communications+in+Combinatorics+%26+Optimization%22">Communications in Combinatorics & Optimization</searchLink>. Dec2026, Vol. 11 Issue 4, p1175-1180. 6p.
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  Data: *<searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink><br />*<searchLink fieldCode="DE" term="%22Bipartite+graphs%22">Bipartite graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: A classic result in domination theory is that a regular graph has in- dependent domination number at most half the order. We strengthen this result to \almost-regular" graphs by showing that if a graph has minimum degree d > 0 and maximum degree at most d + 3, and the subgraph induced by the vertices of degree d +3 (if any) is bipartite, then the independent domination number is at most half the order. We also discuss related questions. [ABSTRACT FROM AUTHOR]
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        Value: 10.22049/cco.2026.31146.2756
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        Text: English
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      – SubjectFull: Regular graphs
        Type: general
      – SubjectFull: Dominating set
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      – SubjectFull: Bipartite graphs
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              Text: Dec2026
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              Y: 2026
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