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.

We apply support vector learning to attributed graphs where the kernel matrices are based on approximations of the Schur-Hadamard inner product. The evaluation of the Schur-Hadamard inner product for a pair of graphs requires the determination of an optimal match between their nodes and edges. It is therefore efficiently approximated by means of recurrent neural networks. The optimal mapping in...

recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $mathcal{v}-$capable if and only if each of its‎ ‎factors is $mathcal{v}-$capable for some varieties $mathcal{v}$‎. ‎in this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎moreover‎, ‎we conclude some results for $mathcal{v}-$capability of direct products of infinitel...

Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a no...

In a recent paper we showed that every connected graph can be written as a weak cartesian product of a family of indecomposable rooted graphs and that this decomposition is unique to within isomorphisms. Using this unique prime factorization theorem we prove that if a graph X can be written as a product of connected rooted graphs, which are pairwise relatively prime, then the automorphism group...

By combining the notions of interval-valued m-polar fuzzy graphs and graphs, notion cubic is first introduced. Then, degree a vertex in complete defined. After that, concepts direct product strong are given. Moreover, weak isomorphism co-weak defined, examples given to prove that not an isomorphism. Finally, complement presented.

the hosoya index and the merrifield-simmons index are two types of graph invariants used in mathematical chemistry. in this paper, we give some formulas for computed these indices for some classes of corona product and link of two graphs. furthermore, we obtain exact formulas of hosoya and merrifield-simmons indices for the set of bicyclic graphs, caterpillars and dual star.

Let [Formula: see text] be an integer. From a set of text]-dimensional vectors, we obtain text]-dot by letting each vector correspond to vertex and adding edge between two vertices if only their dot product text], for some fixed, positive threshold text]. Dot graphs can used model social networks. Recognizing graph is known NP -hard all fixed To understand the position in landscape classes, con...