Algorithm of the Cyclic-Order Graph Program 
				(Implementation and Usage)

Berežný, Štefan; Buša, Ján

doi:10.26456/mmg/2019-731

Cited by 8 publications

(10 citation statements)

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“…Clancy et al [19] also placed an asterisk on a number of the results in their survey to essentially indicate that the mentioned results appeared in journals, which do not have a sufficiently rigorous peer-review process. In certain parts of the presented proofs, it is also possible to simplify the procedure with the help of software generating all cyclic permutations of five elements and its description can be found in Berežný and Buša [20].…”

Section: Introductionmentioning

confidence: 99%

The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

Staš

2021

Mathematics

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The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph K1,1,3\e obtained by removing one edge e incident with some vertex of order two from the complete tripartite graph K1,1,3. The proofs are done with the help of well-known exact values for the crossing numbers of the join products of subgraphs of the considered graph with paths and cycles. Finally, by adding some edges to the graph under consideration, we obtain the crossing numbers of the join products of other graphs with the paths and the cycles on n vertices.

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Section: Introductionmentioning

confidence: 99%

The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

Staš

2021

Mathematics

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“…Some of the ideas and methods were used for the first time in [3,11]. In [2,12,13], the properties of cyclic permutations are verified with the help of the software described in [1]. In our opinion, the methods used in [6,8,9] do not suffice for establishing the crossing number of the join product G * + D n .…”

Section: Michal Stašmentioning

confidence: 99%

“…In our opinion, the methods used in [6,8,9] do not suffice for establishing the crossing number of the join product G * + D n . Some parts of proofs can be done with the help of software that generates all cyclic permutations in [1]. C++ version of the program is located also on the website http://web.tuke.sk/fei-km/coga/.…”

Section: Michal Stašmentioning

confidence: 99%

“…In the proof of the main theorem, the following statements related to some restricted drawings will be helpful. 1) Let T x and T y be two different subgraphs represented by their rot(tx) and rot(ty) of length m, m ≥ 3. If the minimum number of interchanges of adjacent elements of rot(tx) required to produce rot(ty) is at most z, then cr…”

Section: The Crossing Number Of G * + D Nmentioning

confidence: 99%

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On the crossing numbers of join products of five graphs of order six with the discrete graph

Staš¹

2020

Opuscula Math.

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The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G * + Dn, where the disconnected graph G * of order six consists of one isolated vertex and of one edge joining two nonadjacent vertices of the 5-cycle. In our proof, the idea of cyclic permutations and their combinatorial properties will be used. Finally, by adding new edges to the graph G * , the crossing numbers of Gi + Dn for four other graphs Gi of order six will be also established.

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“…The properties of cyclic permutations have been already verified with the help of software by Berežný and Staš in [3] and [4]. Also in this article, some parts of proofs can be simplified by utilizing the work of the software COGA that generates all cyclic permutations by Berežný and Buša [2]. C++ version of the program is located on the website http://web.tuke.sk/fei-km/coga/.…”

Section: Introductionmentioning

confidence: 98%

Determining crossing numbers of the join products of two specific graphs of order six with the discrete graph

Staš

2020

Filomat

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The main aim of the paper is to give the crossing number of the join product G* + Dn for the connected graph G* of order six consisting of P4 + D1 and of one leaf incident with some inner vertex of the path P4 on four vertices, and where Dn consists of n isolated vertices. In the proofs, it will be extend the idea of the minimum numbers of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph G* onto the set of subgraphs by which the edges of G* are crossed exactly once. Due to the mentioned algebraic topological approach, we are able to extend known results concerning crossing numbers for join products of new graphs. The proofs are done with the help of software that generates all cyclic permutations for a given number k, and creates a new graph COG for calculating the distances between all (k-1)! vertices of the graph. Finally, by adding one edge to the graph G*, we are able to obtain the crossing number of the join product of one other graph with the discrete graph Dn.

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Algorithm of the Cyclic-Order Graph Program (Implementation and Usage)

Cited by 8 publications

References 0 publications

The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

On the crossing numbers of join products of five graphs of order six with the discrete graph

Determining crossing numbers of the join products of two specific graphs of order six with the discrete graph

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