The least point covering and domination numbers of a graph

Sampathkumar, E (1990) The least point covering and domination numbers of a graph. Discrete Mathematics, 86 (1-3). pp. 137-142.

Text savedrecs(24).bib Download (2kB)

Abstract

A set S subset-of V of a graph G = (V, E) is a total point cover (t.p.c.) if S is a point cover containing all isolates of G, if any. The number alpha-t(G) is the minimum cardinality of a t.p.c. A t.p.c. S is a least point cover (l.p.c.) if alpha-t(opening-elbow S closing elbow) less-than-or-equal-to alpha-t(opening elbow S1 closing elbow) for any t.p.c. S1, where opening elbow S closing elbow is the subgraph induced by S. The least point covering number alpha-1(G) of G is the minimum cardinality of a l.p.c. A dominating set D of G is a least dominating set (l.d.s.) if gamma(opening elbow D closing elbow) less-than-or-equal-to gamma(opening elbow D1 closing elbow) for any dominating set D1 (gamma-denotes domination number). The least domination number gamma-1(G) of G is the minimum cardinality of a l.d.s. If gamma-t is the total domination number, we prove among other things: (i) gamma-1 less-than-or-equal-to gamma-t, and (ii) for a tree, gamma-1 less-than-or-equal-to alpha-1.

Item Type:	Article
Subjects:	E Mathematical Science > Mathematics
Divisions:	Department of > Mathematics
Depositing User:	Dr Raju C
Date Deposited:	21 Jan 2021 09:54
Last Modified:	27 Jan 2021 06:02
URI:	http://eprints.uni-mysore.ac.in/id/eprint/14306

Actions (login required)

View Item