In this paper we define and study the distinguishing chromatic number, χD(G), of a graph G, building on the work of Albertson and Collins who studied the distinguishing number. We find χD(G) for various families of graphs and characterize those graphs with χD(G) = |V (G)|, and those trees with the maximum chromatic distingushing number for trees. We prove analogs of Brooks’ Theorem for both the...

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Objetivo: focada na Hermenêutica Jurídica e adequada prestação jurisdicional, a pesquisa objetiva traçar elementos do precedente judicial, como um todo, distinguishing, objeto específico, sob o sistema de precedentes obrigatórios adotado pelo Código Processo Civil brasileiro. O argumento distinção impõe busca sua natureza jurídica, seus limites e, ainda, reforçou importância da atividade interp...

Suppose Γ is a group acting on a set X . A k-labeling of X is a mapping c : X → {1, 2, . . . , k}. A labeling c of X is distinguishing (with respect to the action of Γ) if for any g ∈ Γ, g 6= idX , there exists an element x ∈ X such that c(x) 6= c(g(x)). The distinguishing number, DΓ(X), of the action of Γ on X is the minimum k for which there is a k-labeling which is distinguishing. This paper...

We examine the distinguishing number of the Cartesian product of an arbitrary number of complete graphs. We show that for u1 ≤ · · · ≤ ud the distinguishing number of the Cartesian product of complete graphs of these sizes is either du d e or du 1/s d e + 1 where s = Πd−1 i=1 ui. In most cases, which of these values it is can be explicitly determined.

We analyse several well-known key establishment protocols for mobile communications. The protocols are examined with respect to their security and suitability in mobile environments. In a number of cases weaknesses are pointed out, and in many cases reenements are suggested, either to improve the eeciency or to allow simpliied security analysis.

A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest integer k for which G has a distinguishing k-labeling. In this paper, we apply the principle of inclusion-exclusion and develop recursive formulas to count the number of inequivalent distinguishing k-labelings of a gr...

CRM has changed the way companies handle customer enquiries, advertise and sell their products or manage the entire relationship with their customers. As the power of CRM technology has expanded, companies have come to view it as a resource ever more critical to their success in customer management. CRM technology has delivered great benefits to some firms, even propelling a few into positions ...

Transcriptional regulation is largely enacted by transcription factors (TFs) binding DNA. Large numbers of TF binding motifs have been revealed by ChIP-chip experiments followed by computational DNA motif discovery. However, the success of motif discovery algorithms has been limited when applied to sequences bound in vivo (such as those identified by ChIP-chip) because the observed TF-DNA inter...

The distinguishing number D(G) of a graph is the least integer d such that there is a d-labeling of the vertices of G that is not preserved by any nontrivial automorphism of G. We show that the distinguishing number of the square and higher powers of a connected graph G 6= K2,K3 with respect to the Cartesian product is 2. This result strengthens results of Albertson [1] on powers of prime graph...