Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 1-20.
THE CONNECTED GRAPHS OBTAINED FROM FINITE PROJECTIVE PLANES
Atilla Akpinar
Department of Mathematics, Faculty of Science and Art,
University of Bursa Uludag, Bursa, Turkey
e-mail: aakpinar@uludag.edu.tr
Abstract. In this paper, we give a method of obtaining graphs from
finite projective planes, by using an approach based method of taking each
line of such a plane as a path graph. All the graphs obtained with the
help of this method are connected and some properties of these graphs are
determined.
2020 Mathematics Subject Classification.
05C10, 51E15, 05C38, 05C07.
Key words and phrases. Finite projective plane, path, connected graph, degree sequence.
Full text (PDF) (free access)
DOI: https://doi.org/10.21857/mnlqgcrnxy
References:
- A. Akpinar, On some projective planes of finite order, Gazi University Journal of
Science 18 (2005), 319-329.
- R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory (2nd Edition),
Springer, New York, 2012.
MathSciNet
CrossRef
- N. L. Biggs, E. K. Lloyd and R. J. Wilson, Graph Theory 1736-1936, Oxford University
Press, London, 1986.
MathSciNet
- B. Bollobás, Modern Graph Theory, Springer, New York, 2013.
MathSciNet
CrossRef
- J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. Macmillan, London,
1976.
MathSciNet
- R. C. Bose, Mathematical theory of the symmetrical factorial design, Sankhya 8 (1947),
107-166.
MathSciNet
- R. H. Bruck and H. J. Ryser, The non-existence of certain finite projective planes,
Can. J. Math. 1 (1949), 88-93.
MathSciNet
CrossRef
- I. N. Cangul, A. Y. Gunes, M. Togan and A. S. Cevik, New formulae for Zagreb
indices, AIP Conference Proceedings 1863(1), 300013 (2017).
CrossRef
- I. N. Cangul, A. Y. Gunes, M. Togan and S. Delen, Connectedness of graphs and omega
invariant, in: Proceedings Book of the 2nd Mediterranean International Conference
of Pure & Applied Mathematics and Related Areas (MICOPAM 2019), Université
d'Evry/Université Paris-Saclay, Paris, 2019, pp. 59-62.
- F. O. Erdogan and A. Dayioglu, Projective graphs obtained from projective planes,
Adiyaman University Journal of Science 8 (2018), 115-128.
- H. Hamanaka, A. Nakamoto and Y. Suzuki, Rhombus tilings of an even-sided polygon
and quadrangulations on the projective plane, Graphs Combin. 36 (2020), 561-571.
MathSciNet
CrossRef
- C. W. H. Lam, G. Kolesova and L. Thiel, A computer search for finite projective
planes of order 9, Discrete Math. 92 (1991), 187-195.
MathSciNet
CrossRef
- V. Lokesha, B. S. Shetty, P. S. Ranjini, I. N. Cangul and A. S. Cevik, New bounds for
Randić and GA indices, J. Inequal. Appl. 2013 (2013), 180.
MathSciNet
CrossRef
- V. Lokesha, R. Shruti and A. S. Cevik, On certain topological indices of nanostructures
using Q(G) and R(G) operators, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
67 (2018), 178-187.
MathSciNet
CrossRef
- L. Nebesky, Geodesics and steps in a connected graph, Czechoslovak Math. J. 47
(1997), 149-161.
MathSciNet
CrossRef
- L. Nebesky, The induced paths in a connected graph and a ternary relation determined
by them, Math. Bohem. 127 (2002), 397-408.
MathSciNet
- N. Nisse, Network decontamination, in: Distributed Computing by Mobile Entities,
Lecture Notes in Computer Science 11340, Springer, 2019, pp. 516-548.
CrossRef
- N. Nisse and R. P. Soares, On the monotonicity of process number, Discrete Appl.
Math. 210 (2016), 103-111.
MathSciNet
CrossRef
- P. S. K. Reddy, K. N. Prakasha and K. Gavirangaiah, Minimum dominating color
energy of a graph, International Journal of Mathematical Combinatorics 3 (2017),
22-31.
- P. S. K. Reddy, K. N. Prakasha and K. Gavirangaiah, Minimum equitable dominating
Randić energy of a graph, International J. Math. Combin. 3 (2017), 81-89.
- M. K. Siddiqui, M. Imran and M. A. Iqbal, Molecular descriptors of discrete dynamical
system in fractal and Cayley tree type dendrimers, J. Appl. Math. Comput 61 (2019),
57-72.
MathSciNet
CrossRef
- M. K. Siddiqui, N. A. Rehman and M. Imran, Topological indices of some families of
nanostar dendrimers, Journal of Mathematical NanoScience 8 (2018), 91-103.
CrossRef
- F. W. Stevenson, Projective Planes, WH Freeman Co., San Francisco, 1972.
MathSciNet
- D. B. West, Introduction to Graph Theory, Pearson, 2001.
MathSciNet
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