Counting dominating sets in cactus chains | Zendy

Kristina Borissevich | Zendy; Tomislav Došlić | Zendy

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Counting dominating sets in cactus chains

Author(s) -

Kristina Borissevich,

Tomislav Došlić

Publication year - 2015

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1508847b

Subject(s) - mathematics , cactus , corollary , bivariate analysis , combinatorics , set (abstract data type) , square (algebra) , chain (unit) , generating function , function (biology) , discrete mathematics , statistics , geometry , computer science , botany , physics , astronomy , evolutionary biology , biology , programming language

In this paper we consider the number of dominating sets in cactus chains with triangular and square blocks. We derive and solve the recurrences satisfied by those quantities and investigate their asymptotic behavior. In triangular case we also refine the counting by computing the bivariate generating function. As a corollary, we compute the expected size of a dominating set in a triangular cactus chain of a given length.

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