Results 31 to 40 of about 390,323 (304)
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
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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
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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
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Min-Max Dom-Saturation Number of a Tree [PDF]
, 2010 In this paper we present a dynamic programming algorithm for determining the min-max domsaturation number of a ...
Sudha, S., Arumugam, S.
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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
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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).
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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.
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ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP
Barekeng, 2023 The coprime graph of a finite group , denoted by , is a graph with vertex set such that two distinct vertices and are adjacent if and only if their orders are coprime, i.e., where |x| is the order of x.
Agista Surya Bawana +2 more
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The independent resolving number of a graph [PDF]
Mathematica Bohemica, 2003 Summary: For an ordered set \(W = \{w_1, w_2, \dots , w_k\}\) of vertices in a connected graph \(G\) and a vertex \(v\) of \(G\), the code of \(v\) with respect to \(W\) is the \(k\)-vector \[ c_W (v) = (d (v, w_1), d (v, w_2), \dots , d (v, w_k)). \] The set \(W\) is an independent resolving set for \(G\) if (1) \(W\) is independent in \(G\) and (2 ...
Chartrand, G. +2 more
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Note on the smallest root of the independence polynomial
, 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
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