DIMENSI METRIK SISI PADA GRAF THETA SERAGAM

Lailatul Ulla Safitri, NIM.: 21106010001 (2025) DIMENSI METRIK SISI PADA GRAF THETA SERAGAM. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Let G = (V,E) be a simple connected graph with a vertex set V (G) and an edge set E(G). In this graph, the concept of an edge metric generator is introduced, which is a subset of vertices We ⊆ V (G) such that each edge in the graph has a unique distance representation with respect to We. In other words, for every pair of distinct edges, there exists at least one vertex in We that has a different distance to each edge. The minimum cardinality of an edge metric generator is called the edge metric dimension of the graph. This study adopts a structural graph approach and the concept of distances between edges and vertices to determine the edge metric dimension of a graph. The focus is on theta graphs, which consist of multiple paths connecting two terminal vertices. A uniform theta graph is denoted by θ(n,m), where all m paths connecting the two terminals have the same number of vertices, n, in each path.

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