DIMENSI METRIK LOKAL GRAF ULAR SEGITIGA DAN GRAF HASIL OPERASI KORONA ANTARA GRAF ULAR SEGITIGA DENGAN GRAF LINTASAN ORDE DUA

Jaqueline Widad Zuha, NIM.: 22106010057 (2026) DIMENSI METRIK LOKAL GRAF ULAR SEGITIGA DAN GRAF HASIL OPERASI KORONA ANTARA GRAF ULAR SEGITIGA DENGAN GRAF LINTASAN ORDE DUA. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

Let G be a connected graph with vertex set V (G) and edge set E(G). In graph theory, the concept of distance is also known, defined as the length of the shortest path between two vertices. The utilization of this concept of distance gives rise to new concepts, namely the metric dimension and the local metric dimension. Furthermore, let W � V (G) = fw1;w2; : : : ;wkg be an ordered set with k elements, theb the representation of a vertex v 2 V (G) with respect to W is defined as r(vjW) = (d(v;w1); d(v;w2); : : : ; d(v;wk)): The set W is called a local resolving set of the graph G if for every pair of adjacent vertices u; v 2 V (G), it holds that r(ujW) 6= r(vjW). Moreover, the minimum cardinality of such a set W is called the local metric dimension of G, denoted by dim`(G). The purpose of this study is to determine the metric dimension and the local metric dimension of the triangular snake graph Tn, as well as the local metric dimension of the corona product of the triangular snake graph with the path graph of order two. This research employs a literature study method with an approach based on graph structure and distance analysis. The results show that the metric dimension and the local metric dimension of the triangular snake graph are equal to 2. In addition, the local metric dimension of Tn � P2 is 2n + 1, while that of P2 � Tn is n + 3 for odd n and n + 2 for even n.

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