Reflexive Edge Strength on Slanting Ladder Graph and Corona of Centipede and Null Graph

Assume <em>G</em> is a graph that is simple, undirected, and connected. If every edge label is a positive integer in the range 1 to <em>k</em><sub>e</sub>, and every vertex label is a non-negative even number from 0 to 2<em>k</em><sub>v</sub>, then a graph <em>G</em> is considered to have an edge irregular reflexive <em>k</em>-labeling, where <em>k</em> is defined as the maximum of <em>k</em><sub>e</sub> and 2<em>k</em><sub>v</sub>. The edge weight <em>w</em><sub>t</sub>(<em>ab</em>) in the graph <em>G</em>, for the labeling <em>λ</em>, is defined as the function <em>w</em><sub>t</sub> applied to the edge <em>ab</em>. The symbol <em>res</em>(<em>G</em>) denotes the reflexive edge strength, which is the largest label of the smallest <em>k</em>. The results of this research are as follows: <em>res</em>(<em>SL</em><sub>m</sub>) for <em>m</em>≥2 is ⌈(3<em>m</em>−3)/3⌉ for 3<em>m</em>−3 ≢ 2, 3 (mod 6), and ⌈(3<em>m</em>−3)/3⌉+1 for 3<em>m</em>−3 ≡ 2, 3 (mod 6). <em>res</em>(<em>Cp</em><sub>n</sub> ⊙ <em>N</em><sub>m</sub>) for <em>n</em>≥2, <em>m</em>≥1 is ⌈(2<em>nm</em>+2<em>n</em>−1)/3⌉ for 2<em>nm</em>+2<em>n</em>−1 ≢ 2, 3 (mod 6), and ⌈(2<em>nm</em>+2<em>n</em>−1)/3⌉+1 for 2<em>nm</em>+2<em>n</em>−1 ≡ 2, 3 (mod 6).