A three colors competition model on (Z) governed by directed last passage percolation is considered. A stochastic domination argument between subtrees of the last passage percolation tree is put forward. Applied to the case of exponential random times, it allows us to prove that coexistence is possible, i.e. three unbounded colored areas occur with positive probability. Furthermore, asymptotic ...

The bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smallest set E of edges of G such that the graph G − E has domination number greater than that of G. In this paper we present a simplified proof that b(G) ≤ min{8,∆(G) + 2} for all planar graphs G, give examples of planar graphs with bondage number 6, and bound the bondage number of directed graphs.

Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique c...

BackgroundGame Theory Interpretation MethodsRandomizationFunctional Lagrange Multipliers ConclusionsReferences

Let G be a directed graph on n vertices. The domination polynomial of is the D(G, x) =∑ni=0 d(G, i)xi, where i) number dominating sets with i In this paper, we prove that can obtained by using an ordinary generating function. Besides, show our method useful to obtain minimum-weighted set graph.

Domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This thesis focuses on domination theory, and the main aim of the study is to apply a probabilistic approach to obtain new upper bounds for various domination parameters. Chapters 2 and ...

In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination number is equal to the domination num...

In this paper, we introduce the closed domination in graphs. Some interesting relationships are known between domination and closed domination and between closed domination and the independent domination. It is also shown that any triple m, k and n of positive integers with 3 ≤ m ≤ k ≤ n are realizable as the domination number, closed domination number and independent domination number, respect...

the negritude movement reached the crux of its popularity in 1960s. thinkers of this movement to defy the constant development of imperial cultural domination employed the discourse of the colonizer. for instance, they appropriated the binary oppositions which were initially propagated by colonialism but disarranged the hierarchies of importance, beauty and po wer in them. a dance of the for es...