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Retractions and homomorphisms on some operations of graphs. (English) Zbl 1487.05222

Summary: The aim of the present article is to introduce and study a new type of operations on graph, namely, edge graph. The relation between the homomorphisms and retractions on edge graphs is deduced. The limit retractions on the edge graphs are presented. Retractions on a finite number of edge graphs are obtained.

MSC:

05C76 Graph operations (line graphs, products, etc.)
57M05 Fundamental group, presentations, free differential calculus

References:

[1] Abu-Saleem, M., Folding on the wedge sum of graphs and their fundamental group, APPS. Applied Sciences, 12, 14-19 (2010) · Zbl 1194.05135
[2] Abu-Saleem, M., Dynamical manifold and their fundamental group, Advanced Studies in Contemporary Mathematics, 20, 1, 125-131 (2010) · Zbl 1195.57005
[3] Abu-Saleem, M., Conditional fractional folding of a manifold and their fundamental group, Advanced Studies in Contemporary Mathematics, 20, 2, 271-277 (2010) · Zbl 1195.57051
[4] Abu-Saleem, M., On dynamical chaotic de Sitter spaces and their deformation retracts, Proceedings of the Jangjeon Mathematical Society. Memoirs of the Jangjeon Mathematical Society, 14, 2, 231-238 (2011) · Zbl 1228.37054
[5] Abu-Saleem, M., On the dynamical hyperbolic 3-spaces and their deformation retracts, Proceedings of the Jangjeon Mathematical Society. Memoirs of the Jangjeon Mathematical Society, 15, 2, 189-193 (2012) · Zbl 1254.37021
[6] Abu-Saleem, M., On chaotic homotopy group, Advanced Studies in Contemporary Mathematics, 23, 1, 69-75 (2013) · Zbl 1351.55012
[7] Hell, P.; Nešetřil, J., Graphs and Homomorphisms, 28 (2004), Oxford, UK: Oxford University Press, Oxford, UK · Zbl 1062.05139 · doi:10.1093/acprof:oso/9780198528173.001.0001
[8] Pirzada, S.; Dharwadker, A., Applications of Graph Theory, J.KSIAM, 11, 4, 19-38 (2007) · doi:10.1002/pamm.200700981
[9] White, A. T., Graphs, Groups and Surfaces (1973), Amsterdam, Holland: North-Holland Publishing Co., Amsterdam, Holland · Zbl 0268.05102
[10] Wilson, R. J.; Watkins, J. J., Graphs, An Introductory Approuch, A First Course in Discrete Mahematics (1990), Canada John Wiley and sons, Inc. · Zbl 0712.05001
[11] Chartrand, G.; Zhang, P., Chromatic Graph Theory (2009), Taylor and Francis group · Zbl 1169.05001
[12] Hahn, G.; Tardif, C., Graph homomorphisms: structure and symmetry, Graph symmetry. Graph symmetry, NATO ASI Series C 497, 497, 107-166 (1997), Kluwer · Zbl 0880.05079 · doi:10.1007/978-94-015-8937-6_4
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