On the incidence graph of circular spaces
Abstract
A configuration of the triple (P,L,I) is an incidence relation which has the properties "any two points are incident with at most one line" and "any two lines are incident with at most one point". In projective geometry, bipartite graphs can be used as an incidence model between the points and lines of a configuration. The graphs associated with a space are a good tool for understanding the topological and geometric properties of space in abstract systems. In this paper we focus on the incidence graph of circular space and obtain its properties in terms of some pure graph invariants. We also characterize it in terms of the graphs associated with other spaces in the literature.
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PDFDOI: http://dx.doi.org/10.5614/ejgta.2024.12.2.15
References
F. W. Levi, Finite geometrical systems: six public lectues delivered in February, 1940, at the University of Calcutta, (1942).
J. Hauschild, J. Ortiz and O. Vega, On the Levi graph of point-line configurations, Involve, a Journal of Mathematics 8 (5) (2015) 893-900.
V.R. Kulli, The neighborhood graph of a graph, International Journal of Fuzzy Mathematical Archive, 8 (2) (2015) 93-99.
R. Sunar and I. Günaltili, On The Basic Properties of Linear Graphs-I, Konuralp Journal of Mathematics, 9 (1) (2021) 154-158.
I. Günaltili and A. Kurtulus, On finite near-circular spaces, Applied Sciences 6 (2004) 21-26.
I. Günaltili, Z. Akca and S. Olgun, On finite circular spaces, Applied Sciences 8 (2006) 85-90.
T. Heger and M. Takats, Resolving Sets and Semi-Resolving Sets in Finite Projective Planes, Electron. J. Combin. 19 (4) (2012) P30.
D. Bartoli, T. Heger, G. Kiss and M. Takats, On the metric dimension of affine planes, biaffine planes and generalized quadrangles, Australas. J. Combin. 72 (2018) 226–248.
A. Bekes, On the metric dimension of incidence graphs of Möbius planes, Australas. J. Combin. 82 (1) (2022) 59–73.
M.A. Jothi and K. Sankar, On the metric dimension of bipartite graphs, AKCE Int. J. of Graphs and Comb. (2023) 1-4.
F. Harary and R. A. Melter, On the metric dimension of a graph, Ars. Combin. 2 (1976) 191-195.
P.J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci. 22 (1988) 445-455.
G. Chartrand, C. Poisson and P. Zhang, Resolvability and the Upper Dimension of Graphs, Computers and Mathematics with Applications 39 (2000) 19-28.
D.Fitriani and S.W. Saputro, The local metric dimension of amalgamation graphs, Electron. J. Graph Theory Appl. 12 (1) (2024) 125-146.
S. Akhter and R. Farooq, Metric dimension of fullerene graphs, Electron. J. Graph Theory Appl. 7 (1) (2019) 91-103.
E. Hartmann, Planar Circle Geometries: An introduction to Moebius, Laguerre and Minkowski-planes. Springer-Verlag, (2004).
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