LINE REGULAR FUZZY SEMIGRAPHS
This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G* in which σ : V → [0, 1], μ...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2023-03-01
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| Series: | Baghdad Science Journal |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8414 |
| _version_ | 1811162272145342464 |
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| author | ARCHANA S. PREETHI KUTTIPULACKAL |
| author_facet | ARCHANA S. PREETHI KUTTIPULACKAL |
| author_sort | ARCHANA S. |
| collection | DOAJ |
| description |
This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set, μ(u, v) ≤ σ(u) ᴧ σ(v) and η(e) = μ(u1, u2) ᴧ μ(u2, u3) ᴧ … ᴧ μ(un-1, un) ≤ σ(u1) ᴧ σ(un), if e = (u1, u2, …, un), n ≥ 2 is an edge in the semigraph G*, in which a semigraph is defined as a pair of sets (V, X) in which the vertex set V is a non - empty set and edge set X is a set of n – tuples for various n ≥ 2, of distinct elements of V with the properties that, any two elements in the edge set X has at most one vertex in common and for any two edges (ɑ1, ɑ2,…, ɑn ) and (b1, b2,…, bm) in the edge set X are equal if, and only if, n = m and either one of the conditions ɑj = bj or ɑj = bn-j+1 occur for j where the value of j lies between 1 and n. In addition to that edge regularities (line regular and near line regular) and total edge regularities (total line regular and total near line regular) of the corresponding edge degrees and total edge degrees are studied, their properties are examined and a few results connecting vertex regularity and edge regularity of a fuzzy semigraph are obtained.
2020 Mathematics Subject Classification: 05C72, 05C07.
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| first_indexed | 2024-04-10T06:27:16Z |
| format | Article |
| id | doaj.art-6043299d8cfb402ba4d11dc8733c98a5 |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-04-10T06:27:16Z |
| publishDate | 2023-03-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-6043299d8cfb402ba4d11dc8733c98a52023-03-01T19:36:57ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862023-03-01201(SI)10.21123/bsj.2023.8414LINE REGULAR FUZZY SEMIGRAPHSARCHANA S.0PREETHI KUTTIPULACKAL 1Department of Mathematics, University of Calicut, Kerala, India.Department of Mathematics, University of Calicut, Kerala, India. This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set, μ(u, v) ≤ σ(u) ᴧ σ(v) and η(e) = μ(u1, u2) ᴧ μ(u2, u3) ᴧ … ᴧ μ(un-1, un) ≤ σ(u1) ᴧ σ(un), if e = (u1, u2, …, un), n ≥ 2 is an edge in the semigraph G*, in which a semigraph is defined as a pair of sets (V, X) in which the vertex set V is a non - empty set and edge set X is a set of n – tuples for various n ≥ 2, of distinct elements of V with the properties that, any two elements in the edge set X has at most one vertex in common and for any two edges (ɑ1, ɑ2,…, ɑn ) and (b1, b2,…, bm) in the edge set X are equal if, and only if, n = m and either one of the conditions ɑj = bj or ɑj = bn-j+1 occur for j where the value of j lies between 1 and n. In addition to that edge regularities (line regular and near line regular) and total edge regularities (total line regular and total near line regular) of the corresponding edge degrees and total edge degrees are studied, their properties are examined and a few results connecting vertex regularity and edge regularity of a fuzzy semigraph are obtained. 2020 Mathematics Subject Classification: 05C72, 05C07. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8414Fuzzy semigraph, Line degree, Line regular, Near line degree, Semigraph, Total line regular |
| spellingShingle | ARCHANA S. PREETHI KUTTIPULACKAL LINE REGULAR FUZZY SEMIGRAPHS Baghdad Science Journal Fuzzy semigraph, Line degree, Line regular, Near line degree, Semigraph, Total line regular |
| title | LINE REGULAR FUZZY SEMIGRAPHS |
| title_full | LINE REGULAR FUZZY SEMIGRAPHS |
| title_fullStr | LINE REGULAR FUZZY SEMIGRAPHS |
| title_full_unstemmed | LINE REGULAR FUZZY SEMIGRAPHS |
| title_short | LINE REGULAR FUZZY SEMIGRAPHS |
| title_sort | line regular fuzzy semigraphs |
| topic | Fuzzy semigraph, Line degree, Line regular, Near line degree, Semigraph, Total line regular |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8414 |
| work_keys_str_mv | AT archanas lineregularfuzzysemigraphs AT preethikuttipulackal lineregularfuzzysemigraphs |