IJPAM: Volume 77, No. 1 (2012)

CONNECTEDNESS OF ENDO-CAYLEY DIGRAPHS
OF RIGHT(LEFT) ZERO UNION OF SEMIGROUPS

C. Promsakon$^1$, S. Panma$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Chiang Mai University
Chiang Mai, THAILAND
$^1$Centre of Excellence in Mathematics, CHE
Si Ayuttaya Rd., Bangkok 10400, THAILAND
$^2$Materials Science Research Center
Faculty of Science
Chiang Mai University, Chiang Mai, THAILAND


Abstract. Let $S$ be a finite semigroup, $A$ a subset of $S$ and $f$ an endomorphism on $S$. The endo-Cayley digraph of $S$ corresponding to a connecting set $A$ and an endomorphism $f$, denoted by $endo-Cay_f(S,A)$ is a digraph whose vertex set is $S$ and a vertex $u$ is adjacent to vertex $v$ if and only if $v=f(u)a$ for some $a\in A$.

In this paper, we study about the connected properties of endo-Cayley digraphs of cartesian product between semigroups and right(left) zero semigroups. We show the type of connected that they can be. Moreover, we also generalize endo-Cayley digraphs of that product into tensor product resulting graphs.

Received: February 1, 2012

AMS Subject Classification: 46M05, 05C40, 05C76

Key Words and Phrases: endo-Cayley digraph, right(left) zero union of semigroup, tensor product

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 1