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pro vyhledávání: '"Michael A. Henning"'
Autor:
Teresa W. Haynes, Michael A. Henning
Publikováno v:
Opuscula Mathematica, Vol 44, Iss 4, Pp 543-563 (2024)
A graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield
Externí odkaz:
https://doaj.org/article/e6960c46f3584095ba9a4a52f062eff1
Autor:
Michael A. Henning, Jerzy Topp
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 44, Iss 1, p 47 (2024)
Externí odkaz:
https://doaj.org/article/06d00d2f076249c8b821b37307dcc50e
Autor:
Teresa W. Haynes, Michael A. Henning
Publikováno v:
Opuscula Mathematica, Vol 42, Iss 4, Pp 573-582 (2022)
A set \(S\) of vertices in an isolate-free graph \(G\) is a total dominating set if every vertex in \(G\) is adjacent to a vertex in \(S\). A total dominating set of \(G\) is minimal if it contains no total dominating set of \(G\) as a proper subset.
Externí odkaz:
https://doaj.org/article/ab46518842264960ab34dcff65eab170
Publikováno v:
Opuscula Mathematica, Vol 41, Iss 4, Pp 453-464 (2021)
The (total) connected domination game on a graph \(G\) is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a co
Externí odkaz:
https://doaj.org/article/6b151fbeaa5f48c4820b2e7111b2bfd1
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 43, Iss 3, p 619 (2023)
Externí odkaz:
https://doaj.org/article/4d1fc8a8762540358228475419bc330c
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 43, Iss 3, p 825 (2023)
Externí odkaz:
https://doaj.org/article/d7cc0c11d5f845f0a7e9ed93417d60e4
Autor:
T.W. Haynes, Michael A. Henning
Publikováno v:
Communications in Combinatorics and Optimization, Vol 4, Iss 2, Pp 79-94 (2019)
In this paper, we continue the study of the domination game in graphs introduced by Bre{\v{s}}ar, Klav{\v{z}}ar, and Rall [SIAM J. Discrete Math. 24 (2010) 979--991]. We study the paired-domination version of the domination game which adds a matching
Externí odkaz:
https://doaj.org/article/ab2163221dcc4b3d99e5093a4c8faaa1
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol vol. 23 no. 1, Iss Discrete Algorithms (2021)
A dominating set $D$ of a graph $G$ without isolated vertices is called semipaired dominating set if $D$ can be partitioned into $2$-element subsets such that the vertices in each set are at distance at most $2$. The semipaired domination number, den
Externí odkaz:
https://doaj.org/article/2c5ad7ecdf1a43cda58caf4dbdfb5958
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol Vol. 21 no. 3, Iss Graph Theory (2019)
We propose the conjecture that every tree with order $n$ at least $2$ and total domination number $\gamma_t$ has at most $\left(\frac{n-\frac{\gamma_t}{2}}{\frac{\gamma_t}{2}}\right)^{\frac{\gamma_t}{2}}$ minimum total dominating sets. As a relaxatio
Externí odkaz:
https://doaj.org/article/4382b087fc17461dbbe325fd482c3b81
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol Vol. 19 no. 1, Iss Graph Theory (2017)
A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$. The $2$-domi
Externí odkaz:
https://doaj.org/article/acf9109aa9274ce1924a249232c974eb