A Characterization of Automorphism Group and Strong Endomorphism Monoid on Trees with Diameter less than 4
Article Sidebar
Main Article Content
Abstract
For a graph G, automorphisms and strong endomorphisms on graph G refer to functions of vertex set on graph G with preserving strong connectivity, the property allows the set of these functions, along with the composition operation, to exhibit group and monoid, respectively. This research aims to identify the characteristics of automorphism and strong endomorphism functions on tree graphs with diameters less than 4.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The content within the published articles, including images and tables, is copyrighted by Rajamangala University of Technology Rattanakosin. Any use of the article's content, text, ideas, images, or tables for commercial purposes in various formats requires permission from the journal's editorial board.
Rajamangala University of Technology Rattanakosin permits the use and dissemination of article files under the condition that proper attribution to the journal is provided and the content is not used for commercial purposes.
The opinions and views expressed in the articles are solely those of the respective authors and are not associated with Rajamangala University of Technology Rattanakosin or other faculty members in the university. The authors bear full responsibility for the content of their articles, including any errors, and are responsible for the content and editorial review. The editorial board is not responsible for the content or views expressed in the articles.
References
Frucht, R. (1938). Herstellung von Graphen mit vorgegebener abstrakter Gruppe. Compos Mathematics 6. 239-250.
Frucht, R. (1949). Graphs of degree three with a given abstract group. Canadian J Mathematics. 1. 265-278.
Hedrlin, Z., & Pultr, A. (1964). Relations (graphs) with given finitely generated semigroups. Monatsh Math. 68. 213-217.
Hedrlin, Z., & Pultr, A. (1964). Relations (graphs) with given infinite semigroups. Monatsh Math. 68. 421-425.
Hedrlin, Z., & Pultr, A. (1965). Symmetric relations (undirected graphs) with given semigroups. Monatsh Math. 69. 318-322.
Culik, K. (1958). Zur theorie der graphen. Casopis Pest. Mat. 83. 133-155.
Knauer, U., & Nieporte, M. (1989). Endomorphisms of graphs I. The monoid of strong endomorphisms. Arch. Math. 52. 607-614.
Li, W. (1993). Green's relations on the strong endomorphism monoid of a graph. Semigroup Forum. 47. 209-214.
Pipattanajinda, N., Kim, Y., & Arworn, S. (2019). Naturally ordered strong endomorphisms on graphs. Graphs and Combinatorics. 35. 1619–1632.
นิตย์ รื่นรมย์. (2545). ทฤษฎีกราฟ. สำนักพิมพ์มหาวิทยาลัยรามคำแหง.
Gervacio, S. V., & Rara, H. M. (1989). Non-singular trees. Very Often Graphs, Vol. 2 (Ateneo de Manila University, March 1989).
Gervacio, S. V. (1996). Trees with diameter less than 5 and non-singular complement. Discrete Math. 151. 91–97.
Pipattanajinda, N. (2014). Graph with non-singularity. Far East J. Math. Sciences. 95. 1–17.
Pipattanajinda, N., & Kim, Y. (2015). The non-singularity of looped-trees and complement of trees with diameter 5. The Australasian J. of Combinatorics. 63. 297-313.
Pipattanajinda, N., & Kim, Y. (2015). Trees with diameter 5 and non-singular complement. Advances and Applications in Discrete Mathematics. 16. 111-124.
Knauer, U. (1990). Endomorphism types of trees. Words, Languages and Combinatorics. Kyoto, Japan. 28 – 31 Aug. 1990. 273-287.
Harary, F. (1969). Graph theory. Addison-Wesley. Reading. MA.
Li, W. (2003). Graphs with regular monoids. Discrete Math. 265. 105–118.
Pipattanajinda, N., Knauer, U., Gyurov, B., & Panma, S. (2014). The endomorphisms monoids of graphs of order n with a minimum degree n−3. Algebra Discrete Math. 18(2), 274–294.
Pipattanajinda, N., Knauer, U., Gyurov, B., & Panma, S. (2016). The endomorphism monoids of (n−3)-regular graphs of order n. Algebra Discrete Math. 22(2), 284–300.
Pipattanajinda, N. (2014). The endotype of (n−3)-regular graphs of order n. Southeast Asian Bull. Math. 38, 535–541.
