P. Purwanto, Srilinda Ayu Lestari
Let G be a finite simple graph having vertex set V(G), edge set E(G), number of vertices V(G) = p, number of edges E(G) = q, and A={0,1,2,.., [q2] }. A vertex equitable labeling of G is a vertex labeling f: V(G) A that, induces a bijective edge labeling f*: E(G) {1, 2, 3,.., q} defined by f*(uv) = f(u) + f(v) such that vf(a) - vf(b) = 1 for all a, b A, where vf(a) is the number of vertices v with f(v) = a for a A. A graph is called a vertex equitable graph if it admits a vertex equitable labeling. Let m and n be positif integers. A double broom B(m, n, n) is a tree obtained from a path of length m by joining each vertex of degree 1, vi, i {1, 2}, to n new vertices vi,1, vi,2,.., vi,n. In the literature, the vertex equitable labelings of many classes of graphs have been studied. In this paper we study the vertex equitable labeling of a double broom B(m, n, n). We find that then double broom is a vertex equitable graph. © 2021 Author(s).
Department of Mathematics, Universitas Negeri Malang, Jalan Semarang 5, Malang, 65145, Indonesia
