Endomorphism monoid of diamond product of two common complete bipartite graphs

• Autorzy: Jiarasuksakun T. , Rutjanisarakul T. , Thongjua W.
• Języki publikacji: EN

Abstrakty

EN

An endomorphism of a graph G = (V, E) is a mapping f : V → V such that for all x, y ∈ V if {x, y} ∈ E, then {f (x),f (y)}∈ E. Let End(G) be the class of all endomorphisms of graph G. The diamond product of graph G = (V, E) (denoted by G ◊ G) is a graph defined by the vertex set V (G ◊ G) = End(G) and the edge set E (G ◊ G) ={{f, g} ⊂ End(G)|{f(x), g(x)} ∈ E for all x ∈ V}. Let Km,n be a complete bipartite graph on m + n vertices. This research aims to study the algebraic property of V (Km,n ◊ Km,n) = End(Km,n) after we have found that Km,n ◊ Km,n is also a complete bipartite graph on mmnn + nmmn vertices. The result shows that all of its vertices (endomorphisms) form a noncommutative monoid.

Słowa kluczowe

EN

graph theory; bipartite graph

PL

teoria grafów; graf dwudzielny

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2010
• Tom: Vol. 15
• Strony: 59--66
• Opis fizyczny: Bibliogr. 5 poz., rys.

Twórcy

autor

Jiarasuksakun T.

• Department of Mathematics, Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha-uthit Rd. Bangmod, Thungkru, Bangkok 10140 Thailand

autor

Rutjanisarakul T.

• Department of Mathematics, Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha-uthit Rd. Bangmod, Thungkru, Bangkok 10140 Thailand

autor

Thongjua W.

• Department of Mathematics, Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha-uthit Rd. Bangmod, Thungkru, Bangkok 10140 Thailand

Bibliografia

• [1] Sr. Arworn, P.Wojtylak. Connectedness of Diamond Products, preprint, 2008.
• [2] G. Chartrand, P. Zhang. Introduction to Graph Theory. McGraw-Hill, 2005.
• [3] J. Damnernsawad. Diamond Product of Paths, Master Degree Thesis, ChiangMai University, Thailand, 2007.
• [4] T. Jiarasuksakun, T. Rutjanisarakul, W. Thongjua. Diamond Product of Two Common Complete Bipartite Graphs, Int. Conf. on Algebra and Geometry 2009 (ICAG 2009), Phuket, Thailand, 2009.
• [5] D. West. Introduction to Graph Theory, 2nd edition. Prentice Hall, 2001.