On graph irregularity indices with particular regard to degree deviation
نویسندگان
چکیده
Let G = (V,E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, with vertex degree sequence d1 ? d2 ...? dn. A is said to regular if =... Otherwise it irregular. In many applications problems important know how irregular given is. quantity called deviation S(G) ?ni=1 |di-2m/n| can used as an irregularity measure. Some new lower bounds for are obtained. formula computing bidegreed graphs derived also. Besides, two novel measures introduced.
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 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 کاملClustering Validity Indices Evaluation with Regard to Semantic Homogeneity
Clustering validity indices are methods for examining and assessing the quality of data clustering results. Various studies provide a thorough evaluation of their performance using both synthetic and real-world datasets. In this work, we describe various approaches to the topic of evaluation of a clustering scheme. Moreover, a new solution to a problem of selecting an appropriate clustering val...
متن کاملIrregularity Measures of Graph
Let G = (V,E), V = {1,2, . . . ,n}, be a simple graph without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0, di = d(i). A graph G is regular if and only if d1 = d2 = · · · = dn. A graph invariant I(G) is measure of irregularity of graph G with the property I(G) = 0 if and only ifG is regular, and I(G)> 0 otherwise. In this paper we introduce some new irregularity measures.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2021
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2111689r