On the roots of domination polynomials
WebFig. 1 Domination roots of all connected graphs of order 8 and lies in the closed left half-plane. In the next section we provide an explicit family of bipartite graphs with domination roots in the right half-plane. We then investigate limiting curves for the domination roots for complete bipartite graphs. Finally, we Web24 de mar. de 2024 · On the expected number of real roots of polynomials and exponential sums. Author: Gregorio Malajovich. Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ 21941-909, Brazil.
On the roots of domination polynomials
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Web7 de mai. de 2016 · Related to the roots of total domination polynomials there are a few papers. See [16, 2] for more details. Recently authors in [16] shown that all roots of D t (G, x) ... Web1 de mai. de 2016 · Let G be a graph of order n . A dominating set of G is a subset of vertices of G , say S , such that every vertex in V ( G ) S is adjacent to at least one vertex of S . The domination polynomial of G is the polynomial D ( G , x ) = i = 1 n d ( G , i ) x ...
Web2.1. Real domination roots of friendship graphs It is known that 1 is not a domination root as the number of dominating sets in a graph is always odd [11]. On the other hand, of … Web1 de jan. de 2010 · The roots of the chromatic polynomial, independence polynomial, domination polynomial and total domination polynomials have been studied …
WebThis video covers the roots of domination polynomials, including their location in the complex plane, characteristics of integer roots of domination polynomi... Web31 de mai. de 2016 · Let us now investigate graphs whose domination polynomials have only real roots. More precisely for which graph , is a subset of Also we obtain the …
Web31 de dez. de 2024 · The domination polynomial is defined by D(G,x) =∑dkxk D ( G, x) = ∑ d k x k where dk d k is the number of dominating sets in G G with cardinality k k. In this paper we show that the closure of the real roots of domination polynomials is …
WebThe domination polynomials and their roots dominationroots) have been of significant interest over the last 10 years(c.f. [2]). Alikhani characterized graphs with two, three and four distinct domination roots [1, 3]. In [10] Oboudi gave a degree dependent bound on the modulus of domination roots for a laundromat in gulf shores alabamaWeb14 de mar. de 2024 · It is natural to guess that the phenomenon described in Theorem 1.1 is in fact universal in the sense that the theorem holds true for a wide class of coefficients distribution, and not just for Gaussians. In this regard, it is natural (and also suggested in []) to conjecture that Theorem 1.1 holds for random Littlewood polynomials, that is, when … justin bieber agent contact infoWeb8 de jan. de 2014 · We study the domination polynomials of this family of graphs, and in particular examine the domination roots of the family, and find the limiting curve for the roots ... Also we construct some families of graphs whose real domination roots are only $-2$ and $0$. Finally, we conclude by discussing the domination polynomials of a ... justin bieber album my world 2.0 downloadWeb30 de dez. de 2024 · In this paper, we completely determine the domination roots of all graphs with exactly three distinct domination roots. Also, we show that for every forest … laundromat in green bay wiWeb31 de jan. de 2024 · A root of D i (G, x) is called an independence domination root. We investigate the independent domination polynomials of some generalized compound graphs. As consequence, we construct graphs whose independence domination roots are real. Also, we consider some graphs related to paths and study the number of their … laundromat in high springs floridaWebpolynomials. Finally we study graphs with exactly two total domination roots {−3,0}, {−2,0} and {−1,0} in Section 4. 2 Irrelevant edges The easiest recurrence relation for total domination polynomial of a graph is to remove an edge and to compute the total domination polynomial of the graph arising instead of the one for the original graph. justin bieber all i want is youWeb14 de jan. de 2014 · The roots of domination polynomial is called domination roots. In this article, we compute the domination polynomial and domination roots of all graphs of order less than or equal to 6, and show them in the tables. This atlas has published in the PhD thesis of the first author in 2009 and also in book "Dominating sets and domination … justin bieber acoustic fall