On the genus of pancake network
نویسندگان
چکیده
Both the pancake graph and star graph are Cayley graphs and are especially attractive for parallel processing. They both have sublogarithmic diameter, and are fairly sparse compared to hypercubes. In this paper, we focus on another important property, namely the genus. The genus of a graph is the minimum number of handles needed for drawing the graph on the plane without edges crossing. We will investigate the upper bound and lower bound for the genus of pancake graph and compare these values with the genus of the star graph as well as that of the hypercube.
منابع مشابه
Pancake kidney: An unusual type of renal fusion anomaly found in 99mTc-DMSA renal scintigraphy
A 2.5-year-old boy with a history of the previous incidental finding of an ectopic kidney in ultrasonography was referred to our nuclear medicine center for 99mTc-DMSA renal scintigraphy. The scan showed an unusual type of ectopic fused kidneys on the right side of the lower abdomen. In this anomaly, kidneys were fused completely across the medial portion of both upper and lower pole...
متن کاملEmbedding hypercubes into pancake, cycle prefix and substring reversal networks
Among Cayley graphs on the symmetric group, some that have noticeably low diameter relative to the number of generators involved are the pancake network, burnt pancake network, and cycle prefix network [1,6,7,8]. Another such Cayley graph is the star network, and constructions have been given for one-to-one and one-tomany low dilation embeddings of hypercubes into star networks [11,12,15]. For ...
متن کاملSorting by Prefix Reversals
The pancake problem, which has attracted considerable attention, concerns the number of prefix reversals needed to sort the elements of an arbitrary permutation. The number of prefix reversals to sort permutations is also the diameter of the often studied n-dimensional Pancake network. We consider restricted pancake problem, when only k of the possible n− 1 prefix reversals are allowed.
متن کاملComparing Star and Pancake Networks
Low dilation embeddings are used to compare similarities between star and pancake networks. The pancake network of dimension n, Pn, has n! nodes, one for each permutation, and an undirected edge between permutations (nodes) when some prefix reversal transforms one permutation into the other. The star network of dimension n, Sn, has n! nodes, one for each permutation, and an undirected edge betw...
متن کاملThe Intrepid Waitress Problem
An intrepid waitress leaves a restaurant kitchen with a stack of n different sized pancakes. Before she reaches her patrons, she wishes to iterate through all possible stack orderings using only a spatula and performing flips of various sizes. But is this possible? This problem corresponds to constructing a Hamilton path in the “pancake network”, or equivalently, to find a Gray code for permuta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. Arab J. Inf. Technol.
دوره 8 شماره
صفحات -
تاریخ انتشار 2011