16,681 research outputs found
Protecting a Graph with Mobile Guards
Mobile guards on the vertices of a graph are used to defend it against
attacks on either its vertices or its edges. Various models for this problem
have been proposed. In this survey we describe a number of these models with
particular attention to the case when the attack sequence is infinitely long
and the guards must induce some particular configuration before each attack,
such as a dominating set or a vertex cover. Results from the literature
concerning the number of guards needed to successfully defend a graph in each
of these problems are surveyed.Comment: 29 pages, two figures, surve
On the q-criticality of graphs with respect to secure graph domination
Abstract A subset X of the vertex set of a graph G is a secure dominating set of G if each vertex of G which is not in X is adjacent to some vertex in X and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set (X β {v}) βͺ {u} is again a dominating set of G. The secure domination number of G is the cardinality of a smallest secure dominating set of G. The notion of secure graph domination finds applications in the generic setting where the vertex set of G represents distributed locations in some spatial domain and the edges of G represent links between these locations. Patrolling guards, each stationed at one of these locations, may move along the links in order to protect the graph. A minimum secure dominating set of G then represents a smallest collection of locations at which guards may be stationed so that the entire location complex modelled by G is protected in the sense that if a security concern arises at location u, there will either be a guard stationed at that location who can deal with the problem, or else a guard dealing with the problem from an adjacent location v will still leave the location complex protected after moving from location v to location u in order to deal with the problem. A graph G is q-critical if the smallest arbitrary subset of edges whose removal from G necessarily increases the secure domination number, has cardinality q. The notion of qcriticality is important in applications such as the one mentioned above, because it provides threshold information as to the number of edge failures (perhaps caused by an adversary) that will necessitate the hiring of additional guards to secure the location complex. Denote by β¦n the largest value of q for which q-critical graphs of order n exist. It has previously been established that β¦2 = 1, β¦3 = 2, β¦4 = 4, β¦5 = 6 and β¦6 = 9. In this paper we present a repository of all q-critical graphs of orders 2, 3, 4, 5 and 6 for all admissible values of q and we also establish the previously unknown values β¦7 = 12, β¦8 = 17 and β¦9 = 23. These values support an existing conjecture that β¦n = n 2 β 2n + 5 for all n β₯ 7
Guarding Networks Through Heterogeneous Mobile Guards
In this article, the issue of guarding multi-agent systems against a sequence
of intruder attacks through mobile heterogeneous guards (guards with different
ranges) is discussed. The article makes use of graph theoretic abstractions of
such systems in which agents are the nodes of a graph and edges represent
interconnections between agents. Guards represent specialized mobile agents on
specific nodes with capabilities to successfully detect and respond to an
attack within their guarding range. Using this abstraction, the article
addresses the problem in the context of eternal security problem in graphs.
Eternal security refers to securing all the nodes in a graph against an
infinite sequence of intruder attacks by a certain minimum number of guards.
This paper makes use of heterogeneous guards and addresses all the components
of the eternal security problem including the number of guards, their
deployment and movement strategies. In the proposed solution, a graph is
decomposed into clusters and a guard with appropriate range is then assigned to
each cluster. These guards ensure that all nodes within their corresponding
cluster are being protected at all times, thereby achieving the eternal
security in the graph.Comment: American Control Conference, Chicago, IL, 201
Critical Success Factors for Positive User Experience in Hotel Websites: Applying Herzberg's Two Factor Theory for User Experience Modeling
This research presents the development of a critical success factor matrix
for increasing positive user experience of hotel websites based upon user
ratings. Firstly, a number of critical success factors for web usability have
been identified through the initial literature review. Secondly, hotel websites
were surveyed in terms of critical success factors identified through the
literature review. Thirdly, Herzberg's motivation theory has been applied to
the user rating and the critical success factors were categorized into two
areas. Finally, the critical success factor matrix has been developed using the
two main sets of data.Comment: Journal articl
Secure domination number of -subdivision of graphs
Let be a simple graph. A dominating set of is a subset
such that every vertex not in is adjacent to at least one
vertex in . The cardinality of a smallest dominating set of , denoted by
, is the domination number of . A dominating set is called a
secure dominating set of , if for every , there exists a vertex
such that and is a dominating set of
. The cardinality of a smallest secure dominating set of , denoted by
, is the secure domination number of . For any , the -subdivision of is a simple graph
which is constructed by replacing each edge of with a path of length .
In this paper, we study the secure domination number of -subdivision of .Comment: 10 Pages, 8 Figure
- β¦