On The Total Irregularity Strength of Regular Graphs
Rismawati Ramdani, A.N.M. Salman, Assiyatun Assiyatun Β· Journal of Mathematical and Fundamental Sciences Β· 2015
Let πΊ = (π, πΈ) be a graph. A total labeling π: π βͺ πΈ β {1, 2, β― , π} iscalled a totally irregular total π-labeling of πΊ if every two distinct vertices π₯ andπ¦ in π satisfy π€π(π₯) β π€π(π¦) and every two distinct edges π₯1π₯2 and π¦1π¦2 in πΈsatisfy π€π(π₯1π₯2) β π€π(π¦1π¦2), where π€π(π₯) = π(π₯) + Ξ£π₯π§βπΈ(πΊ) π(π₯π§) andπ€π(π₯1π₯2) = π(π₯1) + π(π₯1π₯2) + π(π₯2). The minimum π for which a graph πΊ hasa totally irregular total π-labeling is called the total irregularity strength of πΊ,denoted by π‘π (πΊ). In this paper, we consider an upper bound on the totalirregularity strength of π copies of a regular graph. Besides that, we give a dual labeling of a totally irregular total π-labeling of a regular graph and we consider the total irregularity strength of π copies of a path on two vertices, π copies of a cycle, and π copies of a prism πΆπ β‘ π2.