TY - JOUR
AU - Lutfiah Zalzabila
AU - Diari Indriati
AU - Titin Martini
PY - 2023/12/18
Y2 - 2024/04/16
TI - EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE
JF - BAREKENG: Jurnal Ilmu Matematika dan Terapan
JA - BAREKENG: J. Math. & App.
VL - 17
IS - 4
SE - Articles
DO - 10.30598/barekengvol17iss4pp1941-1948
UR - https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9077
AB - 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).
ER -