Sum Index and Difference Index of Graph Operations

Let Formula: see text be a nonempty simple graph, with Formula: see text denoting its vertex set and Formula: see text its edge set. For any injective vertex labeling Formula: see text, we introduce two corresponding edge labelings: for each edge Formula: see text, let Formula: see text and Formula: see text. We define the difference index Formula: see text of Formula: see text as the minimum size of the range of Formula: see text, and the sum index Formula: see text as the minimum cardinality of the range of Formula: see text. In this work, we establish computational formulas for the sum index and difference index of graphs resulting from graph operations.