Edge irregular reflexive labeling for the disjoint union of gear graphs and prism graphs

Abstract

In graph theory, a graph is given names-generally a whole number-to edges, vertices, or both in a chart. Formally, given a graph G = (V, E), a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k-labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs.