Endo-Regularity of Generalized Wheel Graphs

Nirutt Pipattanajinda; Ulrich Knauer; Srichan Arworn

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Nirutt Pipattanajinda
Ulrich Knauer
Srichan Arworn

Keywords:

generalized wheel graph, endomorphism, regular, orthodox, completely regular

Abstract

A graph $gif.latex?G$ is endo-regular (endo-orthodox, endo-completely-regular) if the monoid of all endomorphisms on $gif.latex?G$ is regular (orthodox, completely regular respectively). In this paper, we characterize endo-regular (endo-orthodox, endocompletely-regular) of generalized wheel graphs $gif.latex?W_{n}(m)$ . For each $gif.latex?m&space;\geq&space;2$ , we found that the $gif.latex?W_{n}(m)$ is endo-regular (endo-orthodox resp.) if and only if $gif.latex?n$ is odd and $gif.latex?m&space;=&space;2$ and $gif.latex?W_{n}(m)$ is endo-completely-regular if and only if it is $gif.latex?W_{3}(2)$ .

Endo-Regularity of Generalized Wheel Graphs

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