scholarly journals The stabilizing index and cyclic index of the coalescence and Cartesian product of uniform hypergraphs

2022 ◽  
Vol 185 ◽  
pp. 105537
Author(s):  
Yi-Zheng Fan ◽  
Meng-Yu Tian ◽  
Min Li
Keyword(s):  
Cartesian Product ◽  
Uniform Hypergraphs

CARTESIAN PRODUCT ON FUZZY IDEALS OF A TERNARY Γ-SEMIGROUP

2020 ◽  
Vol 9 (3) ◽  
pp. 1189-1195 ◽  
Author(s):  
Y. Bhargavi ◽  
T. Eswarlal ◽  
S. Ragamayi
Keyword(s):  
Cartesian Product

scholarly journals Rainbow matchings for 3-uniform hypergraphs

2021 ◽  
Vol 183 ◽  
pp. 105489
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Xiaofan Yuan
Keyword(s):  
Uniform Hypergraphs

scholarly journals Hypercycle Systems of 5-Cycles in Complete 3-Uniform Hypergraphs

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 484
Author(s):  
Anita Keszler ◽  
Zsolt Tuza
Keyword(s):  
Element Subset ◽  
Uniform Hypergraphs ◽  
Vertex Set ◽  
Recursive Constructions

In this paper, we consider the problem of constructing hypercycle systems of 5-cycles in complete 3-uniform hypergraphs. A hypercycle system C(r,k,v) of order v is a collection of r-uniform k-cycles on a v-element vertex set, such that each r-element subset is an edge in precisely one of those k-cycles. We present cyclic hypercycle systems C(3,5,v) of orders v=25,26,31,35,37,41,46,47,55,56, a highly symmetric construction for v=40, and cyclic 2-split constructions of orders 32,40,50,52. As a consequence, all orders v≤60 permitted by the divisibility conditions admit a C(3,5,v) system. New recursive constructions are also introduced.

scholarly journals THE GENERAL POSITION NUMBER OF THE CARTESIAN PRODUCT OF TWO TREES

2020 ◽  
pp. 1-10
Author(s):  
JING TIAN ◽  
KEXIANG XU ◽  
SANDI KLAVŽAR
Keyword(s):  
Shortest Path ◽  
Connected Graph ◽  
General Position ◽  
Cartesian Product

Abstract The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.

scholarly journals Peg Solitaire on Cartesian Products of Graphs

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes
Keyword(s):  
Cartesian Product ◽  
Cartesian Products ◽  
Connected Graphs ◽  
Grid Graphs ◽  
Cartesian Products Of Graphs

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.

s-strongly perfect cartesian product of graphs

1992 ◽  
Vol 16 (4) ◽  
pp. 297-303
Author(s):  
Elefterie Olaru ◽  
Eugen M??ndrescu
Keyword(s):  
Cartesian Product ◽  
Cartesian Product Of Graphs ◽  
Product Of Graphs

PROPERTIES OF QUASI-RELABELING TREE BIMORPHISMS

2010 ◽  
Vol 21 (03) ◽  
pp. 257-276 ◽  
Author(s):  
ANDREAS MALETTI ◽  
CĂTĂLIN IONUŢ TÎRNĂUCĂ
Keyword(s):  
Cartesian Product ◽  
Canonical Representation ◽  
Finite Union ◽  
Top Down ◽  
Tree Language ◽  
Regular Tree ◽  
Fundamental Properties ◽  
Tree Transducers ◽  
Tree Languages ◽  
Context Free

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is defined by a tree bimorphism (φ, L, ψ), where φ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under finite union. However, QUASI is not closed under intersection and complement. In addition, many standard relations on trees (e.g., branches, subtrees, v-product, v-quotient, and f-top-catenation) are not quasi-relabeling relations. If quasi-relabeling relations are considered as string relations (by taking the yields of the trees), then every Cartesian product of two context-free string languages is a quasi-relabeling relation. Finally, the connections between quasi-relabeling relations, alphabetic relations, and classes of tree relations defined by several types of top-down tree transducers are presented. These connections yield that quasi-relabeling relations preserve the regular and algebraic tree languages.

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