in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

Fibonacci cubes and Lucas have been studied as alternatives for the classical hypercube topology interconnection networks. These families of graphs interesting graph theoretic enumerative properties. Among many generalization are $k$-Fibonacci cubes, which same number vertices but edge sets determined by a parameter $k$. In this work, we consider $k$-Lucas obtained subgraphs in way that from cu...

A wealth of geometric and combinatorial properties of a given linear endomorphism X of IR is captured in the study of its associated zonotope Z(X), and, by duality, its associated hyperplane arrangement H(X). This well-known line of study is particularly interesting in case n := rankX ≪ N . We enhance this study to an algebraic level, and associate X with three algebraic structures, referred he...

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...