4,442 research outputs found
New bounds on the signed total domination number of graphs
In this paper, we study the signed total domination number in graphs and
present new sharp lower and upper bounds for this parameter. For example by
making use of the classic theorem of Turan, we present a sharp lower bound on
this parameter for graphs with no complete graph of order r+1 as a subgraph.
Also, we prove that n-2(s-s') is an upper bound on the signed total domination
number of any tree of order n with s support vertices and s' support vertives
of degree two. Moreover, we characterize all trees attainig this bound.Comment: This paper contains 11 pages and one figur
On the inverse signed total domination number in graphs
In this paper, we study the inverse signed total domination number in graphs
and present new lower and upper bounds on this parameter. For example by making
use of the classic theorem of Turan (1941), we present a sharp upper bound for
graphs with no induced complete subgraph of order greater than two. Also, we
bound this parameter for a tree in terms of its order and the number of leaves
and characterize all trees attaining this bound
Open k-monopolies in graphs: complexity and related concepts
Closed monopolies in graphs have a quite long range of applications in
several problems related to overcoming failures, since they frequently have
some common approaches around the notion of majorities, for instance to
consensus problems, diagnosis problems or voting systems. We introduce here
open -monopolies in graphs which are closely related to different parameters
in graphs. Given a graph and , if is the
number of neighbors has in , is an integer and is a positive
integer, then we establish in this article a connection between the following
three concepts:
- Given a nonempty set a vertex of is said to be
-controlled by if . The set
is called an open -monopoly for if it -controls every vertex of
.
- A function is called a signed total
-dominating function for if for all
.
- A nonempty set is a global (defensive and offensive)
-alliance in if holds for every .
In this article we prove that the problem of computing the minimum
cardinality of an open -monopoly in a graph is NP-complete even restricted
to bipartite or chordal graphs. In addition we present some general bounds for
the minimum cardinality of open -monopolies and we derive some exact values.Comment: 18 pages, Discrete Mathematics & Theoretical Computer Science (2016
Remarks on minus (signed) total domination in graphs
Author name used in this publication: T.C.E. ChengAuthor name also used in this publication: E.F. Shan2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
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