Geodetic domination integrity in graphs

Reciprocal version of product degree distance of cactus graphs Let G be a simple graph. A subset S ⊆ V (G) is a said to be a geodetic set if every vertex u /∈ S lies on a shortest path between two vertices from S. The minimum cardinality of such a set S is the geodetic number g(G) of G. A subset D ⊆ V (G) is a dominating set of G if every vertex u /∈ D has at least one neighbor in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset is said to be a geodetic dominating set of G if it is both a geodetic and a dominating set. The geodetic domination number γg(G) is the minimum cardinality among all geodetic dominating sets in G. The geodetic domination integrity of a graph G is defined by DIg(G) = min{|S| + m(G − S) : S is a geodetic dominating set of G}, where m(G − S) denotes the order of the largest component in G−S. In this paper, we study the concepts of geodetic dominating integrity of some families of graphs and derive some bounds for the geodetic domination integrity. Also we obtain geodetic domination integrity of some cartesian product of graphs.Publisher's Versio

Participatory Ecosystem Management Planning at Tuzla Lake (Turkey) Using Fuzzy Cognitive Mapping

A participatory environmental management plan was prepared for Tuzla Lake, Turkey. Fuzzy cognitive mapping approach was used to obtain stakeholder views and desires. Cognitive maps were prepared with 44 stakeholders (villagers, local decisionmakers, government and non-government organization (NGO) officials). Graph theory indices, statistical methods and "What-if" simulations were used in the analysis. The most mentioned variables were livelihood, agriculture and animal husbandry. The most central variable was agriculture for local people (villagers and local decisionmakers) and education for NGO & Government officials. All the stakeholders agreed that livelihood was increased by agriculture and animal husbandry while hunting decreased birds and wildlife. Although local people focused on their livelihoods, NGO & Government officials focused on conservation of Tuzla Lake and education of local people. Stakeholders indicated that the conservation status of Tuzla Lake should be strengthened to conserve the ecosystem and biodiversity, which may be negatively impacted by agriculture and irrigation. Stakeholders mentioned salt extraction, ecotourism, and carpet weaving as alternative economic activities. Cognitive mapping provided an effective tool for the inclusion of the stakeholders' views and ensured initial participation in environmental planning and policy making.Comment: 43 pages, 4 figure

Hub-integrity of splitting graph and duplication of graph elements

The hub-integrity of a graph G = (V (G), E(G)) is denoted as HI(G) and defined by HI(G) = min{|S| + m(G − S), S is a hub set of G}, where m(G − S) is the order of a maximum component of G − S. In this paper, we discuss hub-integrity of splitting graph and duplication of an edge by vertex and duplication of vertex by an edge of some graphs.Publisher's Versio

Domination integrity of total graphs

The domination integrity of a simple connected graph G is a measure of vulnerability of a graph. Here we determine the domination integrity of total graphs of path Pn, cycle Cn and star K1,n.Publisher's Versio

Multi-hop Byzantine reliable broadcast with honest dealer made practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g., digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment

Graph Transformations and Game Theory: A Generative Mechanism for Network Formation

Many systems can be described in terms of networks with characteristic structural properties. To better understand the formation and the dynamics of complex networks one can develop generative models. We propose here a generative model (named dynamic spatial game) that combines graph transformations and game theory. The idea is that a complex network is obtained by a sequence of node-based transformations determined by the interactions of nodes present in the network. We model the node-based transformations by using graph grammars and the interactions between the nodes by using game theory. We illustrate dynamic spatial games on a couple of examples: the role of cooperation in tissue formation and tumor development and the emergence of patterns during the formation of ecological networks