Distance-related Properties of Corona of Certain Graphs

A graph G is called a m−eccentric point graph if each point of G has exactly m ≥ 1 eccentric points. When m = 1, G is called a unique eccentric point (u.e.p) graph. Using the notion of corona of graphs, we show that there exists a m−eccentric point graph for every m ≥ 1. Also, the eccentric graph Ge of a graph G is a graph with the same points as those of G and in which two points u and v are adjacent if and only if either u is an eccentric point of v or v is an eccentric point of u in G. We obtain the structure of the eccentric graph of corona G ◦ H of self-centered or non-self-centered u.e.p graph G with any other graph H and obtain its domination number

On The Center Sets and Center Numbers of Some Graph Classes

For a set $S$ of vertices and the vertex $v$ in a connected graph $G$, $\displaystyle\max_{x \in S}d(x,v)$ is called the $S$-eccentricity of $v$ in $G$. The set of vertices with minimum $S$-eccentricity is called the $S$-center of $G$. Any set $A$ of vertices of $G$ such that $A$ is an $S$-center for some set $S$ of vertices of $G$ is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, $K_{m,n}$, $K_n-e$, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Gravitational waves from spinning eccentric binaries

This paper is to introduce a new software called CBwaves which provides a fast and accurate computational tool to determine the gravitational waveforms yielded by generic spinning binaries of neutron stars and/or black holes on eccentric orbits. This is done within the post-Newtonian (PN) framework by integrating the equations of motion and the spin precession equations while the radiation field is determined by a simultaneous evaluation of the analytic waveforms. In applying CBwaves various physically interesting scenarios have been investigated. In particular, we have studied the appropriateness of the adiabatic approximation, and justified that the energy balance relation is indeed insensitive to the specific form of the applied radiation reaction term. By studying eccentric binary systems it is demonstrated that circular template banks are very ineffective in identifying binaries even if they possess tiny residual orbital eccentricity. In addition, by investigating the validity of the energy balance relation we show that, on contrary to the general expectations, the post-Newtonian approximation should not be applied once the post-Newtonian parameter gets beyond the critical value $\sim 0.08-0.1$. Finally, by studying the early phase of the gravitational waves emitted by strongly eccentric binary systems---which could be formed e.g. in various many-body interactions in the galactic halo---we have found that they possess very specific characteristics which may be used to identify these type of binary systems.Comment: 37 pages, 18 figures, submitted to Class. Quantum Gra

QCSP on partially reflexive forests

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating condition is related firstly to connectivity, and thereafter to accessibility from all vertices of H to connected reflexive subgraphs. In the case of partially reflexive paths, we give a refinement of our dichotomy: QCSP(H) is either in NL or is Pspace-complete