On Exponential Domination of Graphs
Başlık:
On Exponential Domination of Graphs
Yazar:
Dairyko, Michael, author.
ISBN:
9780438072466
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (80 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Michael Young; Leslie Hogben Committee members: Steve Butler; Bernard Lidicky; James Rossmanith.
Özet:
Exponential domination in graphs evaluates the influence that a particular vertex exerts on the remaining vertices within a graph. The amount of influence a vertex exerts is measured through an exponential decay formula with a growth factor of one-half. An exponential dominating set consists of vertices who have significant influence on other vertices. In non-porous exponential domination, vertices in an exponential domination set block the influence of each other. Whereas in porous exponential domination, the influence of exponential dominating vertices are not blocked. For a graph G, the non-porous and porous exponential domination numbers, denoted gammae( G), and gammae(G) are defined to be the cardinality of the minimum non-porous exponential dominating set and cardinality of the minimum porous exponential dominating set, respectively. This dissertation focuses on determining lower and upper bounds of the non-porous and porous exponential domination number of the King grid Kn, Slant grid Sn n-dimensional hypercube Qn, and the general consecutive circulant graph Cn,[l].
A method to determine the lower bound of the non-porous exponential domination number for any graph is derived. In particular, a lower bound for gamma e(Qn) is found. An upper bound for gamma e(Qn) is established through exploiting distance properties of Qn. For any grid graph G, linear programming can be incorporated with the lower bound method to determine a general lower bound for gammae(G). Applying this technique to the grid graphs Kn and Sn yields lower bounds for gammae Kn and gammaeSn. Upper bound constructions for gammaeK n and gammaeSn are also derived. Finally, it is shown that Cn,[l] = Cn,[l].
Notlar:
School code: 0097
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(679345.1) | 679345-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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