Results 71 to 80 of about 11,159 (184)
Introduction to total dominator edge chromatic number
, 2018 We introduce the total dominator edge chromatic number of a graph $G$. A total dominator edge coloring (briefly TDE-coloring) of $G$ is a proper edge coloring of $G$ in which each edge of the graph is adjacent to every edge of some color class. The total dominator edge chromatic number (briefly TDEC-number) $ '^t_d(G)$ of $G$ is the minimum number of ...
Alikhani, Saeid, Ghanbari, Nima
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A New Upper Bound on the Total Domination Number of a Graph [PDF]
, 2007 Michael A. Henning, Anders Yeo
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On upper bounds for total k-domination number via the probabilistic method [PDF]
, 2023 Saylí Sigarreta +2 more
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On the total domatic number of regular graphs [PDF]
Transactions on Combinatorics, 2012 A set S of vertices of a graph G = (V;E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S.
H. Aram +2 more
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Lower bounds on the signed (total) $k$-domination number depending on the clique number
Communications in Combinatorics and Optimization, 2018 Let $G$ be a graph with vertex set $V(G)$. For any integer $k\ge 1$, a signed (total) $k$-dominating function is a function $f: V(G) \rightarrow \{ -1, 1\}$ satisfying $\sum_{x\in N[v]}f(x)\ge k$ ($\sum_{x\in N(v)}f(x)\ge k$) for every $v ...
L. Volkmann
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Total domination numbers of cartesian products
Mathematical communications, 2004 Let $G\Box H$ denote the cartesian product of graphs G and H. Here we determine the total domination numbers of $P_5\Box P_n$ and $P_6\Box P_n$.
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On the number of minimum dominating sets and total dominating sets in forests
Journal of Graph TheoryAbstractWe show that the maximum number of minimum dominating sets of a forest with domination number is at most and construct for each a tree with domination number that has more than minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach.
Jan Petr, Julien Portier, Leo Versteegen
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On the (total) Roman domination in Latin square graphs
AIMS MathematicsLatin square, also known as Latin square matrix, refers to a kind of $ n\times n $ matrix, in which there are exactly $ n $ different symbols and each symbol appears exactly once in each row and column.
Chang-Xu Zhang +2 more
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