A Note On The Partition Dimension of Thorn of Fan Graph
AbstractLet be a connected graph and. For a vertex and an ordered k-partition of, the presentation of concerning is the k-vector, where denotes the distance between and for. The k-partition is said to be resolving if for every two vertices, the representation. The minimum k for which there is a resolving k-partition of is called the partition dimension of, denoted by. Let be a non-negative integer, for. The thorn of, with parameters is obtained by attaching vertices of degree one to the vertex, denoted by. In this paper, we determine the partition dimension of where, the fan on n+1 vertices, for.
G. Chartrand, S. E, and Z. P, "The Partition dimension of a graph," Aequationes Math, pp. 45-54, 2000.
J. A. Bondy and U. Murty, Graph Theory with Applications, London, 1976.
A. "Partition dimension of amalgamation," Bulletin of Mathematics, pp. 161-167, 2012.
A. Kirlangic, "The Scattering number of thorn graph," International Journal of computer math, pp. 299-311, 2004.
E. Baskoro and D., "The partition dimension of corona product of two graphs," Far East J. Math. Sci, pp. 181-196, 2012.
N. L. Biggs, R. Lloyd and R. Wilson, Graph theory, Oxford: 1736-1936, 1986.
G. Chartrand and S. E, "On partition dimension of a graph," Congr. number, pp. 157-168, 1998.
E. Rahimah, L. Yulianti, and D. Welyyanti, "Penentuan Bilangan Kromatik Lokasi Graf Thorn dari Graf Roda W3," Jurnal Matematika UNAND, Vol. VII, No. 4, pp. 1-8, .
J. Gross and J. Yellen, Graph theory and its applications (Second Edition), New York, 2006.
I. Gutman, "Distance in Thorny Graph," Publ.Ins.Math, pp. 31-36, 1998.
D. O. Haryeni, E. T. Baskoro, and S. W. Saputro, "On the partition dimension of disconnected graphs," 2017.
A. Juan, V. Rodriguez and L. Magdalena, "On the partition dimension of trees," discrete applied mathematics, pp. 204-209, 2014.
E. Lloyd, J. Bondy and U. Murt, "Graph theory with apllication," the mathematical gazette, pp. 62-63, 2007.
R. Munir, Matematika Diskrit, Bandung, 2003.
I. Tomescu, I. Javaid and S. , "On the Partition Dimension and Conected Partition dimension of wheels," Ars Combinatoria, pp. 311-317, 2007.
I. Tomescu, "Discrepancies between metric dimension of a connected graph," Discrete Math, pp. 5026-5031, 2008.
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