Abstract Understanding relationships between different products in a market system and predicting how changes design impact their position can be instrumental for companies to create better products. We propose graph neural network-based method modeling products, where nodes network represent edges relationships. Our enables systematic way predict the relationship links unseen future years. Whe...

For many interesting design problems the solution is most naturally represented as a type of graph. This paper proposes that the problem of evolving spring-mass models for a set of design challenges makes an excellent test-bed for evaluating the performance of various graph encoding schemes. We describe how the problem is set up, and introduce a planar graph coding scheme. Results demonstrate t...

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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.