H-E-Super magic graceful labelings of graphs: H-E-SMGL - Duraisamy, Kumar; M. Elakkiya; J. Sebastian Lawrance; M. Bhuvaneshwari (Communications in Mathematics and Applications, 2025)
Let G be a simple graph with p vertices and q edges. A simple graph G admits an H-covering in E(G) belongs to a subgraph of G isomorphic to H. The graph G is said to be H-magic if there exists an one one onto μ from V(G) E(G) onto → { 1,2 , …, p + q } such that for every subgraph H^’ of G isomorphic to H, _v V(H^’) μ(v) + _e E(H^’) μ(e) = M for some positive integer M. An H-E-super magic graceful labeling (H-E-SMGL) is an one one onto μ from V(G) E(G) onto → { 1,2 , …, p + q } with the condition that μ(E(G)) = { 1,2 , …, q} such that, _v V(H^’) μ(v) - _e E(H^’) μ(e) = M. In this paper, we study H-E-SMGL of fans, graphs obtained by joining a star K_1,n with one isolated vertex, books and grids.