منابع مشابه
On graph irregularity strength
An assignment of positive integer weights to the edges of a simple graph G is called irregular, if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal weight, minimized over all irregular assignments. In this study, we show that s(G) c1 n / , for graphs with maximum degree n and minimum
متن کاملAn iterative approach to graph irregularity strength
An assignment of positive integer weights to the edges of a simple graph G is called irregular if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal edge weight, minimized over all irregular assignments, and is set to infinity if no such assignment is possible. In this paper, we take an iterative approach to calculating the irregularity stren...
متن کاملOn the Total Irregularity Strength of Generalized Petersen Graph
As a standard notation, assume that G = G(V,E) is a finite, simple and undirected graph with p vertices and q edges. A labeling of a graph is any mapping that sends some set of graph elements to a set of numbers (usually positive integers). If the domain is the vertex-set or the edge-set, the labelings are called respectively vertex-labelings or edge-labelings. If the domain is V ∪E then we cal...
متن کاملOn the Variance-Type Graph Irregularity Measures
Bell's degree-variance Var$!{}_{B}$ for a graph $G$, with the degree sequence ($d_1,d_2,cdots,d_n$) and size $m$, is defined as$Var!_{B} (G)=frac{1}{n} sum _{i=1}^{n}left[d_{i} -frac{2m}{n}right]^{2}$.In this paper, a new version of the irregularity measures of variance-type, denoted by $Var_q$, is introduced and discussed. Based on a comparative study, it is demonstrated that the n...
متن کامل240 on Graphs of Irregularity Strength 2
We consider undirected graphs without loops or multiple edges. A weighting of a graph G is an assignment of a positive integer w( e) to each edge of G. For a vertex x€V(G), the (weighted) degree d(x) is the sum ofweights on the edges ofG incident to x. The irregularity strength s( G) of a graph G was introduced by Chartrand et al. in [1] a.s the minimum integer t such that G has a weighting wit...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2002
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.10056