@article{discovery10112671,
         journal = {Australasian Journal of Combinatorics},
          number = {2},
            year = {2014},
           title = {Edge growth in graph powers},
           pages = {347--357},
            note = {This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.},
           month = {January},
          volume = {58},
          author = {Pokrovskiy, A},
        abstract = {For a graph G, its rth power G is defined as the graph with the same vertex set as G, and an edge between any two vertices whenever they are within distance r of each other in G. Motivated by a result from additive number theory, Hegarty raised the question of how many new edges G has when G is a regular, connected graph with diameter at least r. We address this question for r {$\neq$} 3, 6. We give a lower bound for the number of edges in the rth power of G in terms of the order of G and the minimal degree of G. As a corollary, for r {$\neq$}3, 6, we determine how small the ratio e(G )/e(G) can be for regular, connected graphs of diameter at least r. r r r},
             url = {https://ajc.maths.uq.edu.au/pdf/58/ajc\%5fv58\%5fp347.pdf},
            issn = {2202-3518}
}