On Constructing H-Irregularity Labeling with Minimum Label for Certain Balloon Graphs

If ϱ and H are simple, connected, undirected graphs, and ϱ can be covered by an H-covering, then for a positive integer p, a total p-labeling φ on ϱ is considered as a total H-irregular p-labeling if, for every subgraph K of ϱ that is isomorphic to H, the weight of K (the sum of the labels of all vertices and edges of K) is a unique number. The smallest integer p for which graph ϱ can be labeled with a total H-irregular p-labeling is called the total H-irregularity strength of graph G. This paper presents the exact total H-irregularity strength values for some particular graphs including balloon graphs, double balloon graphs, and double balloon ladder graphs.