Naslov
K-domination sets on some extremal hexagonal chains

Autori
Majstorović, Snježana ; Klobučar, Antoaneta

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
International Course & Conference on the Interfaces among Mathematics, Chemistry & Computer Sciences

Mjesto i datum
Dubrovnik, Hrvatska, 07.06.2010. - 12.06.2010

Vrsta sudjelovanja
Poster

Vrsta recenzije
Nije recenziran

Ključne riječi
k-dominating set; k-domination number; linear hexagonal chain; zig-zag chain; helicence chain
(k-dominating set; k-domination number; linear hexagonal chain; zig-zag chain; helicence chain.)

Sažetak
Hexagonal systems are geometric objects obtained by arranging mutually congruent regular hexagons in the plane. They are of considerable importance in theoretical chemistry because they are natural graph representation of benzenoid hydrocarbons. A hexagonal chain is a catacondensed hexagonal system in which every hexagon is adjacent to at most two hexagons. In chemistry important topological invariants such as Hosoya index, Merrifield Simmons index and the largest eigenvalue, were investigated on hexagonal chains, and it has been shown that there are three special types of hexagonal chains which are extremal ones due to these invariants. Those are: the linear chain L_h, the zig-zag chain Z_h and the helicence chain H_h, where h is the number of hexagons in a chain. For any graph G by V(G) and E(G) we denote the vertex-set and the edge-set of G, respectively. For graph G subset D of the vertex-set of G is called k-dominating set, k ≥ 1, if for every vertex v ∈ V (G) \D, there exists at least one vertex w ∈ D, such that d(v, w) ≤ k. The k-domination number k(G) is the cardinality of the smallest k-dominating set. The 1-domination set (number) is also called domination set (number). K-dominating sets and k-domination number were already determined for L_h. In this paper we determine k-dominating sets and upper bounds for k-domination number for Z_h and C_h.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Kemija

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