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...

Let d(u, v) denote the distance between two distinct vertices of a connected graph G, and diam(G) be the diameter of G. A radio labeling c of G is an assignment of positive integers to the vertices of G satisfying d(u, v) + |c(u) − c(v)| ≥ diam(G) + 1. The maximum integer in the range of the labeling is its span. The radio number of G, rn(G), is the minimum possible span. The family of gear gra...

Robertson and Seymour (1990) proved that graphs of bounded tree-width are well-quasi-ordered by the graph minor relation. By extending their arguments, Geelen, Gerards, and Whittle (2002) proved that binary matroids of bounded branch-width are well-quasi-ordered by the matroid minor relation. We prove another theorem of this kind in terms of rank-width and vertex-minors. For a graph G = (V,E) a...

We relate the tree-decompositions of hypergraphs introduced by Robertson and Seymour to the finite and infinité algebraic expressions introduced by Bauderon and Courcelle. We express minor inclusion in monadic second-order logic, and we obtain grammatical characterizations of certain sets of graphs defined by excluded minors. We show how tree-decompositions can be used to construct quadratic al...

Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.