Given an undirected graph G and an integer d ≥ 0, the NP-hard BoundedDegree Vertex Deletion problem asks to delete as few vertices as possible from G such that the resulting graph has maximum vertex degree d. Our main result is to prove that Bounded-Degree Vertex Deletion is W[1]-hard with respect to the parameter treewidth. As a side result, we obtain that the NP-hard Vector Dominating Set pro...

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...

angiotensin i-converting enzyme (ace) gene polymorphism; genotype dd or d allele may be involved with an increased susceptibility to type 2 diabetes and diabetic nephropathy (dn). we examined the frequency of ace gene polymorphism in 170 patients (85 type 2 diabetes with nephropathy and 85 without it) in tehran, iran. dna was extracted from the white blood cells and the i/d polymorphism of the ...

a 9 bp deletion between cytochrome oxidase subunit ii and trna lys genes in mitochondrial dna, has proven to be an extremely informative marker for tracing population history. using the pcr-page and pcr-sscp techniques in this study, 152 dna samples collected from iranian populations were screened for the 9 bp deletion. no deletion was observed. a length polymorphism, most probably a 9 bp tripl...

In an edge modi cation problem one has to change the edge set of a given graph as little as possible so as to satisfy a certain property. We prove the NP-hardness of a variety of edge modi cation problems with respect to some well-studied classes of graphs. These include perfect, chordal, chain, comparability, split and asteroidal triple free. We show that some of these problems become polynomi...

A triangle-free graph is maximal if the addition of any edge creates a triangle. For n ~> 5, we show there is an n-node m-edge maximal triangle-free graph if and only if it is complete bipartite or 2n-5<<.m<<.L(n-1)2/4J+l. A diameter 2 graph is minimal if the deletion of any edge increases the diameter. We show that a triangle-free graph is maximal if and only if it is minimal of diameter 2. Fo...

We study the equivalence relation on the set of acyclic orientations of an undirected graph Γ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in tur...

Given a fixed graph H, the H-Free Edge Deletion (resp., Completion, Editing) problems ask whether it is possible to delete from (resp., add to, delete from or add to) the input graph at most k edges so that the resulting graph is H-free, i.e., contains no induced subgraph isomorphic to H. These H-free edge modification problems are well known to be FPT for every fixed H. In this paper, we study...

A graph G = (V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u, v) ∈ E iff u and v are at distance at most 3 in T . The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for n...

We consider the problem of maintaining the strongly connected components (SCCs) of an n-nodes and medges directed graph that undergoes a sequence of edge deletions. Recently, in SODA 2011, Łącki presented a deterministic algorithm that preprocess the graph in O(mn) time and creates a data structure that maintains the SCCs of a graph under edge deletions with a total update time of O(mn). The da...