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Highly irregular graphs with extreme numbers of edges

Highly irregular graphs with extreme numbers of edges,10.1016/S0012-365X(96)00056-8,Discrete Mathematics,Zofia Majcher,Jerzy Michael

Highly irregular graphs with extreme numbers of edges  
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A simple connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we find: (1) the greatest number of edges of a highly irregular graph with n vertices, where n is an odd integer (for n even this number is given in [1]), (2) the smallest number of edges of a highly irregular graph of given order.
Journal: Discrete Mathematics - DM , vol. 164, no. 1-3, pp. 237-242, 1997
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