Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations a lower-dimension space while preserving the structures and semantics for downstream tasks (e.g., node/graph classification, node clustering, link prediction), has drawn considerable attentions recent years. In t...

In power systems, the unintentional outage of a grid element can lead to overload and other equipment and, through domino effect, all or large part system may collapse. The resulting events are called cascading, consecutive, sequential failures. So far, various methods have been proposed identify initial cascading failures with different levels accuracy computational load. this paper, an effect...

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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.