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.