Constructions of Large Graphs on Surfaces
نویسندگان
چکیده
We consider the degree/diameter problem for graphs embedded in a surface, namely, given a surface Σ and integers ∆ and k, determine the maximum order N(∆, k,Σ) of a graph embeddable in Σ with maximum degree ∆ and diameter k. We introduce a number of constructions which produce many new largest known planar and toroidal graphs. We record all these graphs in the available tables of largest known graphs. Given a surface Σ of Euler genus g and an odd diameter k, the current best asymptotic lower bound for N(∆, k,Σ) is given by
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 30 شماره
صفحات -
تاریخ انتشار 2014