Results 21 to 30 of about 9,781,779 (300)
Semi Square Stable Graphs and Efficient Dominating Sets [PDF]
Transactions on Combinatorics, 2023 A graph $G$ is called semi square stable if $\alpha (G^{2})=i(G)$ where $%\alpha (G^{2})$ is the independence number of $G^{2}$ and $i(G)$ is the independent dominating number of $G$.
Baha̓ Abughazaleh, Omar Abughneim
doaj +1 more source
On the $k$-independence number of graphs
Discret. Math., 2018 © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Abiad, Aida +2 more
openaire +4 more sources
Relations between the distinguishing number and some other graph parameters [PDF]
ریاضی و جامعهA distinguishing coloring of a simple graph $G$ is a vertex coloring of $G$ which is preserved only by the identity automorphism of $G$. In other words, this coloring ``breaks'' all symmetries of $G$.
Bahman Ahmadi +1 more
doaj +1 more source
Coloring Some Finite Sets in ℝn
Discussiones Mathematicae Graph Theory, 2013 This note relates to bounds on the chromatic number χ(ℝn) of the Euclidean space, which is the minimum number of colors needed to color all the points in ℝn so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn
Balogh József +2 more
doaj +1 more source
Connected Domination Number and a New Invariant in Graphs with Independence Number Three [PDF]
Computer Science Journal of Moldova, 2021 Adding a connected dominating set of vertices to a graph $G$ increases its number of Hadwiger $h(G)$. Based on this obvious property in [2] we introduced a new invariant $\eta(G)$ for which $\eta(G)\leq h(G)$. We continue to study its property.
Vladimir Bercov
doaj
Note on the smallest root of the independence polynomial [PDF]
, 2013 One can define the independence polynomial of a graph G as follows. Let i(k)(G) denote the number of independent sets of size k of G, where i(0)(G) = 1. Then the independence polynomial of G is I(G,x) = Sigma(n)(k=0)(-1)(k)i(k)(G)x(k).
Csíkvári, Péter
core +1 more source
On the Number of Independent Sets in a Tree [PDF]
The Electronic Journal of Combinatorics, 2010 We show in a simple way that for any $k,m\in{\Bbb N}$, there exists a tree $T$ such that the number of independent sets of $T$ is congruent to $k$ modulo $m$. This resolves a conjecture of Wagner (Almost all trees have an even number of independent sets, Electron. J. Combin. 16 (2009), # R93).
openaire +2 more sources
On θ-commutators and the corresponding non-commuting graphs
Open Mathematics, 2017 The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other ...
Shalchi S., Erfanian A., Farrokhi DG M.
doaj +1 more source
ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS
Barekeng, 2023 The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of .
Rian Kurnia +5 more
doaj +1 more source
A lower bound on the independence number of a graph in terms of degrees [PDF]
, 2006 For a connected and non-complete graph, a new lower bound on its independence number is proved.
Harant, Jochen, Schiermeyer, Ingo
core +2 more sources