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Total Embedding Distributions of Circular Ladders
Author(s) -
Chen Yichao,
Gross Jonathan L.,
Mansour Toufik
Publication year - 2013
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21690
Subject(s) - mathematics , combinatorics , cartesian product , embedding , graph , graph power , discrete mathematics , graph embedding , path graph , line graph , computer science , artificial intelligence
The total embedding polynomial of a graph G is the bivariate polynomialI G ( x , y ) = ∑ i = 0 ∞ a i x i+∑ j = 1 ∞ b j y j , where a i is the number of embeddings, for i = 0 , 1 , ... , into the orientable surface S i , and b j is the number of embeddings, for j = 1 , 2 , ... , into the nonorientable surface N j . The sequence{ a i ( G )| i ≥ 0 } ⋃ { b j ( 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{ a i ( G )| i ≥ 0 } . The circular ladder graph C L nis the Cartesian productK 2 □ C nof the complete graph on two vertices and the cycle graph on n vertices. In this article, we derive a closed formula for the total embedding distribution of circular ladders.