This paper presents a new approach for intuitive and effective design of periodic symmetric tiles. We observe that planar graphs can effectively represent symmetric tiles and graph drawing provides an intuitive paradigm for designing symmetric tiles. Moreover, based on our theoretical work to represent hexagonal symmetry by rectangular symmetry, we are able to present all symmetric tiles as gra...

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Graph pattern matching(GPM) is an important operation on graph computation. Most existing work assumes that query graph or data graph is static, which is contrary to the fact that graphs in real life are intrinsically dynamic. Therefore, in this paper, we propose a new problem of Time-Constrained Graph Pattern Matching(TCGPM) in a large temporal graph. Different from traditional work, our work ...

the annihilating-ideal graph of a commutative ring $r$ is denoted by $ag(r)$, whose vertices are all nonzero ideals of $r$ with nonzero annihilators and two distinct vertices $i$ and $j$ are adjacent if and only if $ij=0$. in this article, we completely characterize rings $r$ when $gr(ag(r))neq 3$.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

Well-known cipher, like DES, FEAL, IDEA or RC6 gain their security by iterating a cryptographically weak function more times. Data are transformed by reusing the same hardware a wished number of times. The first step of a VLSI cipher implementation is the mapping of the cipher data flow onto the hardware architecture. To prove that each combinational level has by entrance a pseudo-random data, ...

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

We (hopefully) proved the result in the title. 1 Notation By a we understand a tuple (a, . . . , a) and by a −→a the tuple (a0, . . . , an). By an abuse of the notation we sometimes identify a graph with the set of its edges. By a weak near unanimity operation we understand an operation w(x0, . . . , xh−1) such that • w(x, . . . , x) ≈ x and • w(y, x, . . . , x) ≈ w(x, y, . . . , x) ≈ · · · ≈ w...