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Average Degree in Graph Powers
Average Degree Graph Powers
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2011/1/21
The kth power of a simple graph G, denoted Gk, is the graph with vertex set V (G)where two vertices are adjacent if they are within distance k in G. We are interested in nding lower bounds on the ave...
Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree
p-Royden boundary p-harmonic boundary p-harmonic function
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2011/1/20
Let p be a real number greater than one and let be a connected graph of bounded degree. We show that the p-Royden boundary of with the p-harmonic boundary removed is a F-set. We...
Cliques in graphs with bounded minimum degree
Cliques graphs bounded minimum degree
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2010/12/14
Let kr(n, δ) be the minimum number of r-cliques in graphs with n vertices and minimum degree δ. We evaluate kr(n, δ) for δ ≤ 4n/5 and some other cases. Moreover, we give a construction, which we conje...
Ranking and unranking trees with given degree sequences
Ranking and unranking trees given degree sequences
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2010/12/3
In this paper, we provide algorithms to rank and unrank certain degree-restricted classes
of Cayley trees. Speci cally, we consider classes of trees that have a given degree sequence
or a given mult...