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...

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...

Let G be a finite simple graph, let C be a set of colours (in this paper we shall always suppose C ⊆ N) and let f : E(G) → C be an edge colouring of G. The colour set of a vertex v ∈ V (G) with respect to f is the set Sf (v) of colours of edges incident to v. The colouring f is neighbour-distinguishing if it distinguishes any two adjacent vertices by their colour sets, i.e., Sf (u) 6= Sf (v) wh...

The output of RC4 was analyzed using the ”book stack” test for randomness from [7]. It is experimentally shown that the keystream generated from RC4 can be distinguished from random with about 232 output bits.

The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the trivial automorphism of G fixes every vertex in S. The fixing set of a group Γ is the set of all fixing numbers of finite graphs with automorphism group Γ. Several authors have studied the distinguishing number of a graph, the smallest number of labels needed to label G so that the automorphism ...

A compact and highly sensitive interferometric bending sensor (inclinometer) capable of distinguishing the bending or inclination orientation is demonstrated. The device operates in reflection mode and consists of a short segment of photonic crystal fiber (PCF) inserted in conventional single-mode optical fiber (SMF). A microscopic collapsed zone in the PCF-SMF junction allows the excitation an...

DNA identity is highly effective and efficient for distinguishing crop varieties regardless of their phenotypic similarities. To establish DNA identity in ramie, 21 simple sequence repeat primers were amplified in 108 accessions of domestic and exotic ramie germplasms. Sixty polymorphic bands were obtained, with an average of 2.9 bands per locus and 2-8 band types per primer locus (average of 5...

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. However, DEA does not provide more information about the efficient DMUs. One of the interesting research subjects is to discriminate between efficient DMUs. The aim of this paper is ranking all efficient (extreme and non-ex...

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a G, in which no two vertices are incident to edges colored with same set colors. an G called edge-chromatic index. In this paper, I compute index Anti-prism, sunflower graph, double triangular winged prism, rectangular prism and Polygonal snake graph.