Crossing numbers of Sierpinski-like graphs
نویسندگان
چکیده
The crossing number of Sierpiński graphs S(n, k) and their regularizations S(n, k) and S(n, k) is studied. Explicit drawings of these graphs are presented and proved to be optimal for S(n, k) and S(n, k) for every n ≥ 1 and k ≥ 1. These are the first nontrivial families of graphs of “fractal” type whose crossing number is known.
منابع مشابه
Acyclic Edge-coloring of Sierpinski-like Graphs
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by χ′a(G). Sierpinski graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpinski gasket graphs Sn are the graphs naturally defined ...
متن کاملThe Maximum of the Maximum Rectilinear Crossing Numbers of d-Regular Graphs of Order n
We extend known results regarding the maximum rectilinear crossing number of the cycle graph (Cn) and the complete graph (Kn) to the class of general d-regular graphs Rn,d. We present the generalized star drawings of the d-regular graphs Sn,d of order n where n + d ≡ 1 (mod 2) and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of Sn,d for n ≡ d ≡ 0 (mod 2...
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملOn the crossing numbers of Cartesian products of stars and graphs of order six
The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of crossing numbers were obtained. The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are ...
متن کاملThe crossing numbers of products of path with graphs of order six
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G Pn for graphs G of order six are studied. Let H denote the unique tree of order si...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Journal of Graph Theory
دوره 50 شماره
صفحات -
تاریخ انتشار 2005