we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations of chordal graphs into two new characterizations. More intriguingly, these characterizations of chordal graphs can be naturally strengthened to new characterizations of strongly...

The Kneser graph K(m, n) has the n-subsets of {1, 2 . . . . . m} as its vertices, two such vertices being adjacent whenever they are disjoint. The kth multichromatic number of the graph G is the least integer t such that the vertices of G can be assigned k-subsets of {1, 2,... ,t}, so that adjacent vertices of G receive disjoint sets. The values of xk(K(m, n)) are computed for n = 2, 3 and boun...

due to the change of lifestyle and improvement of public health the number of aged people has considerably increased. considering the relationship of the environment and people, the built environment features could exacerbate or facilitate the elderly people’s vulnerability and social needs. recently, a large number of studies have put emphasis on the relationship between the neighborhoods’ ope...

There are various ways to define the chromatic polynomial P (G; z) of a graph G. Perhaps the first that springs to mind is to define it to be the graph invariant P (G; k) with the property that when k is a positive integer P (G; k) is the number of colourings of the vertices of G with k or fewer colours such that adjacent vertices receive different colours. One then has to prove that P (G; k) i...

IZA DP No. 11178 NOVEMBER 2017 Sorting out Neighbourhood Effects Using Sibling Data Previous research has reported evidence of intergenerational transmission of both neighbourhood status and social and economic outcomes later in life; parents influence where their children live as adults and how well they do later in life in terms of their income. However, interactions between the individual, t...

introductionhistoric cities and neighbourhoods in iran couldn’t adjust themselves to quick changes of the recent decades andhave lost their quality in many aspects. regardless of different cultural, economic and social conditions, newneighbourhoods have been formed next to old areas of the cities. although these new areas welcom ed newfunctions, they couldn’t provide suitable environments for t...

Abstract Assuming the generalized Riemann hypothesis, we provide explicit upper bounds for moduli of $$\log {\mathcal {L}(s)}$$ log L ( s ) and $$\mathcal {L}'(s)/\mathcal {L}(s)$$ ′ </mml:ms...

Consider a configuration of pebbles distributed on the vertices of a connected graph of order n. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles on a graph is called solvable if it is possible to place a pebble on any given vertex using a sequence of pebbling steps. The pebbling number of a graph, denot...