zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Dominating sets of centipedes. (English) Zbl 1180.05078
Summary: Let G=(V,E) be a simple graph. A set SV is a dominating set of G, if every vertex in V-S is adjacent to at least one vertex in S. Let 𝒟(G,i) be the family of all dominating sets of a graph G with cardinality i, and G * be the graph obtained by appending a single i pendant edge to each vertex of graph G. We call P n * a centipede, where P n is a path with n vertices. In this paper we study the dominating sets of centipedes and obtain the number of dominating sets of P n * . We show that 𝒟(P n * ,i)=𝒟(C n * ,i)=𝒟(C n * ,i), where C n and G n are respectively, cycle and arbitrary graph of order n.
MSC:
05C69Dominating sets, independent sets, cliques