Partition dimension of graphs with two bridges on rose graphs
Abstract
The partition dimension of a graph G, denoted by pd(G) is a generalization of the metric dimension, in which the distinction between vertices is no longer based on a specific set of vertices, but rather on a partition of the vertex set of the graph. A partition is called a resolving partition if every vertex in the graph has a distinct distance vector representation with respect to each subset in the partition. The minimum cardinality of such a resolving partition is called the partition dimension of the graph. This study focuses on the partition dimension of double bridge graphs constructed from a pair of rose graphs. It is shown that the partition dimension of the double bridge graph obtained from two rose graphs connected by two bridge edges is 4
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PDFDOI: http://dx.doi.org/10.19184/ijc.2026.10.1.2
References
J. A. Bondy and U. S. R. Murty, Graph theory with applications, 1982, New York: Elsevier Science Publishing Co.
G. Chartrand, L. Eroh, M. A. Johnson, and O. R. Oellermann, Resolvability in graphs and the metric dimension of a graph, Discrete Appl. Math., 105, 2000, 99-113.
G. Chartrand, E. Salehi, and P. Zhang, The partition dimension of a graph, Aequationes Math., 59(1), 2000, 45-54.
J. L. Gross, and J. Yellen, Handbook of graph theory, 2004, New York: CRC Press.
K. Koritsoglou, G. Tsoumanis, V. Patras, and I. Fudos, Shortest path algorithms for pedestrian navigation systems, Information, 13(6), 2022, 269.
K. A. Sugeng, P. John, M. L. Lawrence, L. F. Anwar, M. Bača, and A. Semaničová-Fenovčíková, Modular Irregularity Strength on Some Flower Graphs. Electron. J. Graph Theory Appl. (EJGTA), 11(1), 2022, 27-38.
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