In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve problems existing in various disciplines physical sciences like computer sciences, physics, and chemistry. Topological indices (TIs) are one which frequently used identify different physicochemical structural properties molecular graphs. Wiener index is first distance-based TI that c...

We present two short proofs for Diestel's criterion that a connected graph has normal spanning tree provided it contains no subdivision of countable clique in which every edge been replaced by uncountably many parallel edges.

For a graph G and a unary graph operation X, there is a graph sequence {Gk} generated by G0 = G and Gk+1 = X(Gk). Let Sp(Gk) denote the set of normalized Laplacian eigenvalues of Gk. The set of limit points of ⋃∞ k=0 Sp(Gk), lim infk→∞ Sp(Gk) and lim supk→∞ Sp(Gk) are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained tha...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

in this paper, it was shown that , where  and , and , where  is not prime and , are od-characterizable.

In this paper we develop a new description for subdivision surfaces based on a graph grammar formalism. Subdivision schemes are specified by a context sensitive grammar in which production rules represent topological and geometrical transformations to the surface’s control mesh. This methodology can be used for all known subdivision surface schemes. Moreover, it gives an effective representatio...

Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...