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 ...

We study the compositional and configurational heterogeneity of Greater London at city- neighbourhood-scale using Geographic Information System (GIS) data. Urban morphometric indicators are calculated including plan-area indices fractal dimensions land cover, frontal area index buildings, evenness, contagion. To distinguish between city-scale heterogeneity, 720 km 2 is divided into 1 [Formula: ...

STUDY OBJECTIVE To assess the relations between characteristics of the neighbourhood internal and external built environment and past six month and lifetime depression. DESIGN AND SETTING Depression and sociodemographic information were assessed in a cross sectional survey of residents of New York City (NYC). All respondents were geocoded to neighbourhood of residence. Data on the quality of ...

OBJECTIVE The neighbourhood built environment may affect walking behaviour of elders. However, such effects remain underexplored, especially in an Asian context. We examined associations of perceived environmental attributes with overall and neighbourhood-specific walking for transport in a sample of Chinese elders residing in Hong Kong, an ultra-dense Chinese metropolis. DESIGN Cross-section...

Background: There is a lack of research pertaining to the links between built environment attributes and obesity in adults in the Eastern Mediterranean Region. In the Libyan context, no previous studies have been conducted to investigate this relationship. Therefore, the aim of this study was to examine associations between perceived neighbourhood built environmental attributes and obesity amon...

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...