The neighbourhood polynomial G , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. In other word $N(G,x)=sum_{Uin N(G)} x^{|U|}$, where N(G) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. In this paper we compute this polynomial for some na...

Neighbourhood in many Nigerian cities had been designed without proper consideration of design principles, which invariably affect the residents’ quality of life. This s‌tudy assessed the experts' and residents’ perception of design correlates of neighbourhood quality in the urban area of Ibadan. Data were obtained from both primary and secondary sources. A ques‌tionnaire survey and direct obse...

background: this study explored the relationship between socio-economic characteristics at the individual and neighbourhood levels, and wellbeing and lifestyle behaviours of young iranian women. methods: cluster convenience sampling was used to select 391 iranian women participated in this cross-sectional survey in shiraz, iran in 2013. a scale adapted from the british general household social ...

the neighbourhood polynomial g , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. in other word $n(g,x)=sum_{uin n(g)} x^{|u|}$, where n(g) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. in this paper we compute this polynomial for some na...

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The two-player game of Nim on graphs is played on a regular graph with positively weighted edges by moving alternately from a fixed starting vertex to an adjacent vertex, decreasing the weight of the incident edge to a strictly smaller non-negative integer. The game ends when a player is unable to move since all edges incident with the vertex from which the player is to move have weight zero. I...

In the perpetual gossiping problem, introduced by Liestman and Richards, information may be generated at any time and at any vertex of a graph G; adjacent vertices can communicate by telephone calls. We define Wk(G) to be the minimum w such that, placing at most k calls each time unit, we can ensure that every piece of information is known to every vertex within w time units of its generation. ...

We study the minimum number of weights assigned to the edges of a graph G with no component K2 so that any two adjacent vertices have distinct sets of weights on their incident edges. The best possible upper bound on this parameter is proved.