Connected domination polynomial of graphs

• Autorzy: Mojdeh D. A. , Emadi A. S.

Identyfikatory

DOI

10.1515/fascmath-2018-0007

• Języki publikacji: EN

Abstrakty

EN

Let G be a simple graph of order n. The connected domination polynomial of G is the polynomial D_c (G, x) = Σ ^|V(G)|_i=γc(G) d_c (G, i)xⁱ, where d_c (G, i) is the number of connected dominating sets of G of size i and γ_c (G) is the connected domination number of G. In this paper we study D_c (G, x) of any graph. We classify many families of graphs by studying their connected domination polynomial.

Słowa kluczowe

EN

connected domination polynomial; graphs; connected dominating set; petersen graph

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 60
• Strony: 103--121
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Mojdeh D. A.

• Department of Mathematics University of Mazandaran Babolsar, Iran

autor

Emadi A. S.

• Department of Mathematics University of Mazandaran Babolsar, Iran

Bibliografia

• [1] Akbari S., Alikhani S., Peng Y.H., Characterization of graphs using domination Polynomials, European J. Combin., 31(2010), 1714-1724.
• [2] Alikhani S., Peng Y.H., Dominating sets and domination polynomials of cycles, Global Journal of Pure and Applied Mathematics, 4(2)(2008), 151-162.
• [3] Alikhani S., Peng Y.H., Domination polynomials of cubic graphs of order 10, Turkish Journal of Mathematics, 35(2011), 355-366.
• [4] Alikhani S., Peng Y.H., Dominating sets and domination polynomials of Paths, International Journal of Mathematics and Mathematical Science, Vol. 2009, Article ID 542040 (2009).
• [5] Biggs N.L., Algebraic Graph Theory, 2nd ed. Cambridge, Cambridge University press., England, 1993.
• [6] Bondy J.A., Murty U.S.R., Graph Theory, Graduate Texts Mathematics 244, 2008.
• [7] Haynes T.W., Hedetniemi S.T., Slater P.J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).