1 Title

Nonlocal-Adjacency Metric Dimension of Graphs

Abstract. Let  be an ordered subset of the vertex set of a graph , and let  be a vertex in . The adjacency metric  representation of vertex  with respect to the set  is the -vector  The set  is called a nonlocal-adjacency metric resolving set of the graph  if  for every pair of vertices  with  not adjacent to . The minimum cardinality of a nonlocal-adjacency metric resolving set of  is called the nonlocal-adjacency metric dimension of , denoted by . In this paper, we present graphs obtained from the degree corona product of two graphs. The degree corona product of graphs  and , denoted by , is the graph constructed by taking a graph  and  copies  of graph , and then connecting every vertex  to all vertices in , for every  and . Furthermore, we determine and analyze the nonlocal-adjacency metric dimension of basic graphs  centered graphs  and the degree corona product graphs . In addition, we provide upper bounds, characterizations of the nonlocal-adjacency metric dimension of graphs, and examples of applications of this concept. Key words and Phrases: Adjacency metric representation, Nonlocal-adjacency metric resolving set, Nonlocal-adjacency metric dimension, Degree corona product.