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pro vyhledávání: '"Krop Elliot"'
The cordiality game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting \track{unlabeled} vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label on any edg
Externí odkaz:
http://arxiv.org/abs/2403.18060
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 36, Iss 2, Pp 299-308 (2016)
A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant.
Externí odkaz:
https://doaj.org/article/e8799f7e78f045118123d0698de13311
Autor:
Krop Elliot, Krop Irina
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 33, Iss 4, Pp 771-784 (2013)
Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that , sligh
Externí odkaz:
https://doaj.org/article/9107c7fffeb04448b286d283819118fc
Publikováno v:
The Electronic Journal of Combinatorics 28(2) (2021), #P2.12
A maximum sequence $S$ of vertices in a graph $G$, so that every vertex in $S$ has a neighbor which is independent, or is itself independent, from all previous vertices in $S$, is called a Grundy dominating sequence. The Grundy domination number, $\g
Externí odkaz:
http://arxiv.org/abs/2104.05665
Publikováno v:
Theory and Applications of Graphs, 8(2): Article 5, (2021)
In any graph $G$, the domination number $\gamma(G)$ is at most the independence number $\alpha(G)$. The Inverse Domination Conjecture says that, in any isolate-free $G$, there exists pair of vertex-disjoint dominating sets $D, D'$ with $|D|=\gamma(G)
Externí odkaz:
http://arxiv.org/abs/1907.05966
Publikováno v:
Discrete Applied Mathematics 258: 8-12, (2019)
A set of vertices $S$ in a simple isolate-free graph $G$ is a semi-total dominating set of $G$ if it is a dominating set of $G$ and every vertex of $S$ is within distance 2 or less with another vertex of $S$. The semi-total domination number of $G$,
Externí odkaz:
http://arxiv.org/abs/1803.04746
Autor:
Davila, Randy, Krop, Elliot
Publikováno v:
Theory and Applications of Graphs: Vol. 7 : Iss. 1 , Article 4, 2020
Given a simple graph $G$, a dominating set in $G$ is a set of vertices $S$ such that every vertex not in $S$ has a neighbor in $S$. Denote the domination number, which is the size of any minimum dominating set of $G$, by $\gamma(G)$. For any integer
Externí odkaz:
http://arxiv.org/abs/1708.01656
For any graphs $G$ and $H$, we say that a bound is of Vizing-type if $\gamma(G\square H)\geq c \gamma(G)\gamma(H)$ for some constant $c$. We show several bounds of Vizing-type for graphs $G$ with forbidden induced subgraphs. In particular, if $G$ is
Externí odkaz:
http://arxiv.org/abs/1705.04954
Autor:
Krop, Elliot
We show that if $G$ is a cograph, that is $P_4$-free, then for any graph $H$, $\gamma(G\square H)\geq \gamma(G)\gamma(H)$. By the characterization of cographs as a finite sequence of unions and joins of $K_1$, this result easily follows from that of
Externí odkaz:
http://arxiv.org/abs/1609.08370
Autor:
Krop, Elliot
For any graph $G$, we define the power $\pi(G)$ as the minimum of the largest number of neighbors in a $\gamma$-set of $G$, of any vertex, taken over all $\gamma$-sets of $G$. We show that $\gamma(G\square H)\geq \frac{\pi(G)}{2\pi(G) -1}\gamma(G)\ga
Externí odkaz:
http://arxiv.org/abs/1608.02107