symmetric division deg index is one of the 148 discrete adriatic indices that showed good predictive properties on the testing sets provided by international academy of mathematical chemistry.symmetric division deg index is defined by$$sdd(g) = sume left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right),$$where $d_i$ is the degree of vertex $i$ in graph $g$.in this pap...

let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

in this work, using eigenvalues and eigenvectors of unitary cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing pst occurring in its unitary cayley graph. moreover, we have some developments when $r$ is a product of local rings.

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some NP-complete properties such as Hamiltonicity can be decided in polynomial time on digraphs of constant directed treewidth. Nevertheless, despite more than one deca...

Because of the importance of special functions, several books and a large collection of papers have been devoted to the numerical computation of these functions, the most well-known being the NBS handbook by Abramowitz and Stegun. But up to this date, symbolic and numeric environments offer no routines for the validated evaluation of special functions. We point out how a provable correct functi...

Prof. Frederick Jelinek, dr.h.c., Julian Sinclair Smith Professor at theWhiting School of Engineering at the Johns Hopkins University and the director of JHU’s Center for Language Speech and Processing, died unexpectedly at his workplace on Sept. 14, 2010. Prof. Jelinek is survived by his wife Milena Jelinek, professor at Columbia University, son and daughter William and Hannah, three grandchil...

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.

Let CMSO denote the counting monadic second order logic of graphs. We give a constructive proof that for some computable function f , there is an algorithm A that takes as input a CMSO sentence φ, a positive integer t, and a connected graph G of maximum degree at most ∆, and determines, in time f(|φ|, t) · 2O(∆·t) · |G|O(t), whether G has a supergraph G′ of treewidth at most t such that G′ |= φ...

Courcelle, B., The monadic second-order logic of graphs VII: Graphs as relational structures, Theoretical Computer Science 101 (1992) 3-33. Relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied. We define operations on structures that are compatible with monadic second-order logic, and that are powerful enough to represent c...