Open AccessTotal H-irregularity strength of ladder graphs
Author(s) -
Nurdin Hinding,
Elit Vega,
Hasmawati Basir
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1218/1/012026
Subject(s) - algorithm , materials science , computer science
H-irregular total labeling and total H-irregularity strength of graphs were not complete.This research aimed to determine the total H-Irregularity strength of ladder graph L b with subgraphs C 8 and C 10 .To determine of the total H-irregularity strength of ladder graphs, we have to determine the greatest lower bound and the smallest upper bound. The lower bound was analysed based on graph characteristics and other supporting theorems, while the upper bound was analysed by construct a function H-Irregular total labeling. The results reveal that the total H-Irregularity strength of ladder graph L n with subgraph C 8 is ⌈ n − 2 i + 14 16 ⌉ ≤ t h s ( L n , C 8 ) ≤ ⌈ n + 14 18 ⌉ , for 18 i − 15 ≤ n ≤ 18 i + 2 , where i = 1,2, …, N and the total H-Irregularity strength of ladder graph L n with subgraph C 10 is t h s ( G , H ) ≥ max { ⌈ 1 + m 1 − 1 | V ( H / S 1 ) | + | E ( H / S 1 ) | ⌉ , … , ⌈ 1 + m 1 − 1 | V ( H / S z ) | + | E ( H / S z ) | ⌉ } ⌈ n − 3 i + 18 20 ⌉ ≤ t h s ( L n , C 10 ) ≤ ⌈ n + 18 23 ⌉ , for 23 i − 20 ≤ n ≤ 23 i + 2 , where i = 1,2, …, N .