A graph polynomial P (G, x) is called reconstructible if it is uniquely determined by the polynomials of the vertex deleted subgraphs of G for every graph G with at least three vertices. In this note it is shown that subgraph-counting graph polynomials of increasing families of graphs are reconstructible if and only if each graph from the corresponding defining family is reconstructible from it...

The foremost problem in this area of graph theory is the Reconstruction Conjecture which states that a graph is reconstructible from its collection of vertex-deleted subgraphs. In spite of several attempts to prove the conjecture only very partial results have been obtained. Several of these results do however bring to light interesting structural relationships between a graph and its subgraphs...

The reconstruction conjecture has remained open for simple undirected graphs since it was suggested in 1941 by Kelly and Ulam. In an attempt to prove the conjecture, many graph invariants have been shown to be reconstructible from the vertex-deleted deck, and in particular, some prominent graph polynomials. Among these are the Tutte polynomial, the chromatic polynomial and the characteristic po...

We show that the two problems of deciding whether k vertices or k edges can be deleted from a graph to obtain a wheel-free graph is W [2]-hard. This immediately implies that deciding whether k edges can be added to obtain a graph that contains no complement of a wheel as an induced subgraph isW [2]-hard, thereby resolving an open problem of Heggernes et. al. [7] (STOC07) who asks whether there ...

Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many authors. Wide diameter of a graph combines studying connectivity with the diameter of a graph. Diameter with width k of a graph G is defined as the minimum integer d for which there exist at least k i...

Distributed mutual exclusion is a fundamental problem of distributed systems that coordinates the access to critical shared resources. It concerns with how the various distributed processes access to the shared resources in a mutually exclusive manner. This paper presents fully distributed improved token based mutual exclusion algorithm for distributed system. In this algorithm, a process which...

A graph is k-degenerate if its vertices can be successively deleted so that when deleted, each has degree at most k. These graphs were introduced by Lick and White in 1970 and have been studied in several subsequent papers. We present sharp bounds on the diameter of maximal k-degenerate graphs and characterize the extremal graphs for the upper bound. We present a simple characterization of the ...