Lucky Edge Labeling of H Graph, N Copies of H-Graph, Theta Graph, Duplication of Theta Graphs and Path Union of Theta Graphs

• Published in: Annals of the Romanian society for cell biology Vol. 25; no. 2; pp. 4480 - 4497
• Main Authors: Babu, Shalini Rajendra, Ramya, N
• Format: Journal Article
• Language: English
• Published: Arad "Vasile Goldis" Western University Arad, Romania 01.01.2021
• Subjects: Labeling
• ISSN: 2067-3019; 2067-8282

A vertex labeling of a graph G is an assignment of labels to the vertices of G that includes for each edge uv a label depends on the vertex labels x and y. In this paper we proved that the H graphs, n copies of H-graph, Path union of Helm, path union of closed helm, path union of Gear graph are lucky edge labeled graphs. [1,8] Definition 1.4 A vertex V{ is said to be a duplication of ^ if all the vertices which are adjacent to are now adjacent to V{_ [8] Theorem:1 The Theta graph (T«) admits Lucky edge labeling whose Lucky number is 6. Edge set can be defined as, E{G) = {Щиьщщ,и>и1+1]1 <i< 5} Let us define the vertex labeling /: V(G) = (1,2,3,4) labeling has to be given by, i) f(u0) = 4 ii) f(u1) = 1 iii) f(u2) = 2 iv) f(u3) = 4 v) f(u4) = 3 vi) f(u5) = 3 vii) f(u6) = 1 Define the map /· on E as follows, LetГЯ(СМ1,2,3,4Д6} suchthat, i) f·(u0>ui) = 5 ii) Г(и0>щ) = 6 iii) f·(Ui,iLi+1) = i + 1, where 1 < i < 5 vi)r(u6>ui) = 4 Illustration:! Figure-1 shows Theta graph and its lucky number is 6. Theorem:2 The duplication of any vertex of degree 3, in the Theta graph is a Lucky edge labelled graph and its Lucky edge number is 8.