Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T20:05:37.119Z Has data issue: false hasContentIssue false
  • English
  • Français

THE JOIN OF SPLIT GRAPHS WHOSE QUASI-STRONG ENDOMORPHISMS FORM A MONOID

Part of: Graph theory Semigroups

Published online by Cambridge University Press:  27 June 2014

HAILONG HOU ,
RUI GU  and
YOULIN SHANG
HAILONG HOU*
Affiliation:
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan, 471003, PR China email [email protected]
RUI GU
Affiliation:
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan, 471003, PR China
YOULIN SHANG
Affiliation:
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan, 471003, PR China
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we characterise the quasi-strong endomorphisms of the join of split graphs. We give conditions under which the quasi-strong endomorphisms of the join of split graphs form a monoid.

Keywords

quasi-strong endomorphismmonoidsplit graphjoin of graphs

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 1 - 10
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Böttcher, M. and Knauer, U., ‘Endomorphism spectra of graphs’, Discrete Math. 109 (1992), 45–57.CrossRefGoogle Scholar
Fan, S., ‘Retractions of split graphs and End-orthodox split graphs’, Discrete Math. 257 (2002), 161–164.CrossRefGoogle Scholar
Godsil, C. and Royle, G., Algebraic Graph Theory (Springer, New York, 2000).Google Scholar
Hou, H. and Luo, Y., ‘Graphs whose endomorphism monoids are regular’, Discrete Math. 308 (2008), 3888–3896.CrossRefGoogle Scholar
Hou, H., Luo, Y. and Cheng, Z., ‘The endomorphism monoid of Pn’, European J. Combin. 29 (2008), 1173–1185.Google Scholar
Hou, H., Luo, Y. and Fan, X., ‘End-regular and End-orthodox joins of split graphs’, Ars Combin. 105 (2012), 305–318.Google Scholar
Hou, H., Luo, Y. and Gu, R., ‘The join of split graphs whose half-strong endomorphisms form a monoid’, Acta Math. Sin. (Eng. Ser.) 26 (2010), 1139–1148.CrossRefGoogle Scholar
Howie, J. M., Fundamentals of Semigroup Theory (Clarendon Press, Oxford, 1995).CrossRefGoogle Scholar
Kelarev, A., Graph Algebras and Automata (Marcel Dekker, New York, 2003).Google Scholar
Kelarev, A. and Praeger, C. E., ‘On transitive Cayley graphs of groups and semigroups’, European J. Combin. 24 (2003), 59–72.Google Scholar
Kelarev, A., Ryan, J. and Yearwood, J., ‘Cayley graphs as classifiers for data mining: the influence of asymmetries’, Discrete Math. 309 (2009), 5360–5369.Google Scholar
Knauer, U., Algebraic Graph Theory: Morphisms, Monoids and Matrices (De Gruyter, Berlin, 2011).Google Scholar
Li, W., ‘Graphs with regular monoid’, Discrete Math. 265 (2003), 105–118.Google Scholar
Li, W. and Chen, J., ‘Endomorphism-regularity of split graphs’, European J. Combin. 22 (2001), 207–216.CrossRefGoogle Scholar
Luo, Y., Zhang, W., Qin, Y. and Hou, H., ‘Split graphs whose half-strong endomorphisms form a monoid’, Sci. China Math. 55 (2012), 1303–1320.Google Scholar