Trees with maximum number of maximal matchings
نویسندگان
چکیده
منابع مشابه
The number of maximal matchings in polyphenylene chains
A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...
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Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $S$ is a global forcing set for maximal matchings of $G$ if $...
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In this paper, we study lower bounds on the size of maximal and maximum matchings in 3-connected planar graphs and graphs with bounded maximum degree. For each class, we give a lower bound on the size of matchings, and show that the bound is tight for some graph within the class. 1 Research supported by NSERC. 2 Research supported by NSF grant ACR-0222920. Preprint submitted to Elsevier Science...
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A “perfect matching” of a graph G with n vertices is a set of n/2 independent edges of G. In the present study, we succeeded in determining the trees whose complements have the extremal number of “perfect matchings” for two different group of trees. Some further problems are also posed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem 105: 131–141, 2005
متن کاملTrees with maximum p-reinforcement number
Let G = (V , E) be a graph and p a positive integer. The p-domination number γp(G) is the minimum cardinality of a set D ⊆ V with |NG(x) ∩ D| ≥ p for all x ∈ V \ D. The p-reinforcement number rp(G) is the smallest number of edges whose addition to G results in a graph G with γp(G′) < γp(G). It is showed by Lu et al. (2013) that rp(T ) ≤ p + 1 for any tree T and p ≥ 2. This paper characterizes a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.074