On The Total Edge and Vertex Irregularity Strength of Some Graphs Obtained from Star - Rismawati Ramdani; A.N.M Salman; Hilda Assiyatun (IndoMS, 2019)
Let G=(V(G),E(G)) be a graph and k be a positive integer. A total k-labeling of G is a map f: V(G)E(G)→ {1,2,…,k }. The edge weight uv under the labeling f is denoted by w_f(uv) and defined by w_f(uv)=f(u)+f(uv)+f(v). The vertex weight v under the labeling f is denoted by w_f(v) and defined by w_f(v) = f(v) + _uv E(G) f(uv). A total k-labeling of G is called an edge irregular total k-labeling of G if w_f(e_1)≠ w_f(e_2) for every two distinct edges e_1 and e_2 in E(G). The total edge irregularity strength of G, denoted by tes(G), is the minimum k for which G has an edge irregular total k-labeling. A total k-labeling of G is called a vertex irregular total k-labeling of G if w_f(v_1)≠ w_f(v_2) for every two distinct vertices v_1 and v_2 in V(G). The total vertex irregularity strength of G, denoted by tvs(G), is the minimum k for which G has a vertex irregular total k-labeling. In this paper, we determine the total edge irregularity strength and the total vertex irregularity strength of some graphs obtained from star, which are gear, fungus, and some copies of stars.