EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE
Let G in this paper be a connected and simple graph with set V(G) which is called a vertex and E(G) which is called an edge. The edge irregular reflexive k-labeling f on G consist of integers {1,2,3,...,k_e} as edge labels and even integers {0,2,4,...,2k_v} as the label of vertices, k=max{k_e,2k_v},...
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Universitas Pattimura
2023-12-01
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9077 |
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| author | Lutfiah Alifia Zalzabila Diari Indriati Titin Sri Martini |
| author_facet | Lutfiah Alifia Zalzabila Diari Indriati Titin Sri Martini |
| author_sort | Lutfiah Alifia Zalzabila |
| collection | DOAJ |
| description | Let G in this paper be a connected and simple graph with set V(G) which is called a vertex and E(G) which is called an edge. The edge irregular reflexive k-labeling f on G consist of integers {1,2,3,...,k_e} as edge labels and even integers {0,2,4,...,2k_v} as the label of vertices, k=max{k_e,2k_v}, all edge weights are different. The weight of an edge xy in G represented by wt(xy) is defined as wt(xy)= f (x)+ f (xy)+ f (y). The smallest k of graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength, symbolized by res (G). In article, we discuss about edge irregular reflexive k-labeling of alternate triangular snake A(T_n ) and the double alternate quadrilateral snake DA(Q_n ). In this paper, the res of alternate triangular snake A(T_n ) , n≥3 has been obtained. That is ⌈(2n-1)/3⌉ for n even,2n-1≢2,3 (mod 6),⌈(2n-1)/3⌉+1 for n even,2n-1=2,3 (mod 6),⌈(2n-2)/3⌉ for n odd,2n-2≢2,3 (mod 6), and ⌈(2n-2)/3⌉+1 for n odd,2n-2=2,3 (mod 6). Then, the reflexive edge strength of double alternate quadrilateral snake DA (Q_n) ⌈ (4n-1 )/3⌉for n even, 4n - 1 ≠2,3 (mod 6), ⌈ (4n-1 )/3⌉+1 for n even, 4n - 1 = 2,3 (mod 6), ⌈ (4n-4)/3⌉ for n odd, 4n - 4 ≠2,3 (mod 6), and ⌈ (4n-4 )/3⌉+1 for n odd, 4n - 4 = 2,3 (mod 6). |
| format | Article |
| id | doaj-art-be2bf4984e654bf18e419d773f960848 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Universitas Pattimura |
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| series | Barekeng |
| spelling | doaj-art-be2bf4984e654bf18e419d773f9608482025-08-20T03:36:37ZengUniversitas PattimuraBarekeng1978-72272615-30172023-12-011741941194810.30598/barekengvol17iss4pp1941-19489077EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKELutfiah Alifia Zalzabila0Diari Indriati1Titin Sri Martini2Department of Mathematics, Faculty of Mathematics and Natural Sciences, Sebelas Maret University, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Sebelas Maret University, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Sebelas Maret University, IndonesiaLet G in this paper be a connected and simple graph with set V(G) which is called a vertex and E(G) which is called an edge. The edge irregular reflexive k-labeling f on G consist of integers {1,2,3,...,k_e} as edge labels and even integers {0,2,4,...,2k_v} as the label of vertices, k=max{k_e,2k_v}, all edge weights are different. The weight of an edge xy in G represented by wt(xy) is defined as wt(xy)= f (x)+ f (xy)+ f (y). The smallest k of graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength, symbolized by res (G). In article, we discuss about edge irregular reflexive k-labeling of alternate triangular snake A(T_n ) and the double alternate quadrilateral snake DA(Q_n ). In this paper, the res of alternate triangular snake A(T_n ) , n≥3 has been obtained. That is ⌈(2n-1)/3⌉ for n even,2n-1≢2,3 (mod 6),⌈(2n-1)/3⌉+1 for n even,2n-1=2,3 (mod 6),⌈(2n-2)/3⌉ for n odd,2n-2≢2,3 (mod 6), and ⌈(2n-2)/3⌉+1 for n odd,2n-2=2,3 (mod 6). Then, the reflexive edge strength of double alternate quadrilateral snake DA (Q_n) ⌈ (4n-1 )/3⌉for n even, 4n - 1 ≠2,3 (mod 6), ⌈ (4n-1 )/3⌉+1 for n even, 4n - 1 = 2,3 (mod 6), ⌈ (4n-4)/3⌉ for n odd, 4n - 4 ≠2,3 (mod 6), and ⌈ (4n-4 )/3⌉+1 for n odd, 4n - 4 = 2,3 (mod 6).https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9077reflexive edge strengthalternate triangular snakedouble alternate quadrilateral snake |
| spellingShingle | Lutfiah Alifia Zalzabila Diari Indriati Titin Sri Martini EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE Barekeng reflexive edge strength alternate triangular snake double alternate quadrilateral snake |
| title | EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE |
| title_full | EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE |
| title_fullStr | EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE |
| title_full_unstemmed | EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE |
| title_short | EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE |
| title_sort | edge irregular reflexive labeling on alternate triangular snake and double alternate quadrilateral snake |
| topic | reflexive edge strength alternate triangular snake double alternate quadrilateral snake |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9077 |
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