Let G be a graph with two non adjacent vertices and G′ the graph constructed from G by adding an edge between them. It is known that the trace of Q′ is 2 plus the trace of Q, where Q and Q′ are the signless Laplacian matrices of G and G′ respectively. So, the sum of the Q′-eigenvalues of G′ is the sum of the the Qeigenvalues of G plus two. It is said that Q-spectral integral variation occurs wh...

In 2012 Seager introduced a new variant of the Cops and Robbers game, in which a cop searches for a moving robber on a graph using distance probes. The robber on his turn can either remain still or move to an adjacent vertex, while the cop on her turn probes any vertex and learns the robber’s distance from the probed vertex. Carraher, Choi, Delcourt, Erickson and West later showed that for any ...

Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define corona graphs. Given a small simple connected graph which we call basic graph, corona graphs are defined by taking corona product of the basic ...

Residents of socioeconomically deprived areas perceive their neighbourhood as less conducive to healthy behaviours than residents of more affluent areas. Whether these unfavourable perceptions are based on objective neighbourhood features or other factors is poorly understood. We examined individual and contextual correlates of socioeconomic inequalities in neighbourhood perceptions across five...

In graph pebbling games, one considers a distribution of pebbles on the vertices of a graph, and a pebbling move consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The t-pebbling number πt(G) of a graph G is the smallest m such that for every initial distribution of m pebbles on V (G) and every target vertex x there exists a sequence of pebbling moves leading t...

We consider a variation of cop vs. robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on V (G) and moves according to this fixed distribution. The cop moves from vertex to adjacent vertex with the goal of minimizing expected capture time. Players move simultaneously. We show that when the gambler’s distribution...

A graph G is given and two players, a cop and a robber, play the folioking game: the cop chooses a vertex, then the robber chooses a vertex, then the players move alternately beginning with the cop. A move consists of staying at one’s present vertex or moving to an adjacent vertex; each move is seen by both players. The cop wins if he manages to occupy the same vertex as the robber, and the rob...

A simplified frequency integrated radiative transfer equation is solved to study Compton scatterings in the corona of the disk by using numerical iterating method. We find that the vertical thickness of the corona cannot be used as the typical length to measure the optical depth of the corona. A semi-analytical approach is proposed to calculate the energy dissipations in the corona of the disk....

every year, millions of muslims from all over the world, are going to participate in the pilgrimage hajj located in mecca in kingdom of saudi arabia (ksa). the accumulation of many people from all parts of the world in terms of health management is of great importance. in fact, every person could be a carrier of various chronic or acute diseases. this huge population may lead to occurrence of s...

Time series observations at UV (Extreme Ultraviolet Imaging Telescope/Solar and Heliospheric Observatory) and X-ray (Soft X-Ray Telescope/Yohkoh) wavelengths reveal properties of the global solar corona that are not easily identiÐed in a single image. A median-Ðltering technique that rejects features varying with time is used to isolate background corona. The coronal hole boundaries, polar plum...