Genus distributions of star-ladders

نویسندگان

  • Yichao Chen
  • Jonathan L. Gross
  • Toufik Mansour
چکیده

Star-ladder graphs were introduced by Gross in his development of a quadratic-time algorithm for the genus distribution of a cubic outerplanar graph. This paper derives a formula for the genus distribution of star-ladder graphs, using Mohar’s overlap matrix and Chebyshev polynomials. Newly developed methods have led to a number of recent papers that derive genus distributions and total embedding distributions for various families of graphs. Our focus here is on a family of graphs called star-ladders.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Total embedding distributions of Ringel ladders

The total embedding distributions of a graph is consisted of the orientable embeddings and nonorientable embeddings and have been know for few classes of graphs. The genus distribution of Ringel ladders is determined in [Discrete Mathematics 216 (2000) 235-252] by E.H. Tesar. In this paper, the explicit formula for non-orientable embeddings of Ringel ladders is obtained.

متن کامل

Embedding Distributions and Chebyshev Polynomials

The history of genus distributions began with J. Gross et al. in 1980s. Since then, a lot of study has given to this parameter, and the explicit formulas are obtained for various kinds of graphs. In this paper, we find a new usage of Chebyshev polynomials in the study of genus distribution, using the overlap matrix, we obtain homogeneous recurrence relation for rank distribution polynomial, whi...

متن کامل

Total Embedding Distributions of Circular Ladders

where ai is the number of embeddings, for i = 0, 1, . . ., into the orientable surface Si, and bj is the number of embeddings, for j = 1, 2, . . ., into the non-orientable surface Nj . The sequence {ai(G)|i ≥ 0} ⋃ {bj(G)|j ≥ 1} is called the total embedding distribution of the graph G; it is known for relatively few classes of graphs, compared to the genus distribution {ai(G)|i ≥ 0}. The circul...

متن کامل

Genus distributions of graphs under self-edge-amalgamations

We investigate the well-known problem of counting graph imbeddings on all oriented surfaces with a focus on graphs that are obtained by pasting together two root-edges of another base graph. We require that the partitioned genus distribution of the base graph with respect to these root-edges be known and that both root-edges have two 2-valent endpoints. We derive general formulas for calculatin...

متن کامل

Genus Distributions of Cubic Outerplanar Graphs

We present a quadratic-time algorithm for computing the genus distribution of any 3-regular outerplanar graph. Although recursions and some formulas for genus distributions have previously been calculated for bouquets and for various kinds of ladders and other special families of graphs, cubic outerplanar graphs now emerge as the most general family of graphs whose genus distributions are known...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 312  شماره 

صفحات  -

تاریخ انتشار 2012