On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph
In the paper, we extend known results concerning crossing numbers of join products of small graphs of order six with discrete graphs. The crossing number of the join product <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>G</mi&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/1/135 |
| _version_ | 1818039290171490304 |
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| author | Michal Staš |
| author_facet | Michal Staš |
| author_sort | Michal Staš |
| collection | DOAJ |
| description | In the paper, we extend known results concerning crossing numbers of join products of small graphs of order six with discrete graphs. The crossing number of the join product <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>G</mi> <mo>∗</mo> </msup> <mo>+</mo> <msub> <mi>D</mi> <mi>n</mi> </msub> </mrow> </semantics> </math> </inline-formula> for the graph <inline-formula> <math display="inline"> <semantics> <msup> <mi>G</mi> <mo>∗</mo> </msup> </semantics> </math> </inline-formula> on six vertices consists of one vertex which is adjacent with three non-consecutive vertices of the 5-cycle. The proofs were based on the idea of establishing minimum values of crossings between two different subgraphs that cross the edges of the graph <inline-formula> <math display="inline"> <semantics> <msup> <mi>G</mi> <mo>∗</mo> </msup> </semantics> </math> </inline-formula> exactly once. These minimum symmetrical values are described in the individual symmetric tables. |
| first_indexed | 2024-12-10T07:56:17Z |
| format | Article |
| id | doaj.art-91a55db21cc54a73978d34539371cb06 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T07:56:17Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-91a55db21cc54a73978d34539371cb062022-12-22T01:56:53ZengMDPI AGSymmetry2073-89942020-01-0112113510.3390/sym12010135sym12010135On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete GraphMichal Staš0Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, SlovakiaIn the paper, we extend known results concerning crossing numbers of join products of small graphs of order six with discrete graphs. The crossing number of the join product <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>G</mi> <mo>∗</mo> </msup> <mo>+</mo> <msub> <mi>D</mi> <mi>n</mi> </msub> </mrow> </semantics> </math> </inline-formula> for the graph <inline-formula> <math display="inline"> <semantics> <msup> <mi>G</mi> <mo>∗</mo> </msup> </semantics> </math> </inline-formula> on six vertices consists of one vertex which is adjacent with three non-consecutive vertices of the 5-cycle. The proofs were based on the idea of establishing minimum values of crossings between two different subgraphs that cross the edges of the graph <inline-formula> <math display="inline"> <semantics> <msup> <mi>G</mi> <mo>∗</mo> </msup> </semantics> </math> </inline-formula> exactly once. These minimum symmetrical values are described in the individual symmetric tables.https://www.mdpi.com/2073-8994/12/1/135graphgood drawingcrossing numberjoin productcyclic permutation |
| spellingShingle | Michal Staš On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph Symmetry graph good drawing crossing number join product cyclic permutation |
| title | On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph |
| title_full | On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph |
| title_fullStr | On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph |
| title_full_unstemmed | On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph |
| title_short | On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph |
| title_sort | on the crossing numbers of the joining of a specific graph on six vertices with the discrete graph |
| topic | graph good drawing crossing number join product cyclic permutation |
| url | https://www.mdpi.com/2073-8994/12/1/135 |
| work_keys_str_mv | AT michalstas onthecrossingnumbersofthejoiningofaspecificgraphonsixverticeswiththediscretegraph |