In the usual forms of homogeneity analysis (which are also known as multiple correspondence analysis or MCA) the size of a point set is defined as the size of the star plot of the set. The star plot is the graph defined by connecting all points in the set with their centroid, and the size is the total squared length of the edges. In order to prevent trivial solutions the configuration X is usua...

A method for measuring dissimilarities between cyclic strings is introduced. It computes a weighted mean between two (lower and upper) bounds of the exact cyclic edit distance, which are founded on a window-constrained edit graph related to the strings involved. Weights are the ones which minimize the sum of squared relative errors of the weighted solution with respect to exact values, on a tra...

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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.

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.