Edge Irregular Reflexive Labeling for Some Classes of Plane Graphs

• Published in: Malaysian Journal of Mathematical Sciences
• Main Author: Yoong K.K.; Hasni R.; Lau G.C.; Irfan M.
• Format: Article
• Language: English
• Published: Universiti Putra Malaysia 2022
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85129677671&partnerID=40&md5=37d2a048084795a5cedba8247a5637fe

For a graph G, we define a total k-labeling φ as a combination of an edge labeling φ e(x) {1, 2,…, ke} and a vertex labeling φv(x) {0, 2,…, 2kv}, such that φ(x) = φpv (x) if x (Formula presented) V(G) and φ(x) = φe(x) if x (Formula presented) E(G), where k = max {ke, 2kv}. The total k-labeling p is called an edge irregular reflexive k-labeling of G, if for every two edges xy, x'y' of G, one has wt(xy) = wt(x'y'), where wt(xy) = φv (x) + φe(xy) + φv (y). The smallest value of k for which such labeling exists is called a reflexive edge strength of G. In this paper, we study the edge irregular reflexive labeling on plane graphs and determine its reflexive edge strength. © 2022. All Rights Reserved.