Reduced Sombor index of bicyclic graphs

2021 ◽  
Author(s):  
Shiikhar Dorjsembe ◽  
Batmend Horoldagva
Keyword(s):  
Index Formula ◽  
Bicyclic Graphs ◽  
Extremal Properties

The concept of Sombor indices (SO) of a graph was recently introduced by Gutman and the reduced Sombor index [Formula: see text] of a graph [Formula: see text] is defined by [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text]. In this paper, we study the extremal properties of the reduced Sombor index and characterize the bicyclic graphs with extremal [Formula: see text]-value.

On the forgotten topological index of graphs

2020 ◽  
pp. 2150054
Author(s):  
Akbar Jahanbani
Keyword(s):  
Topological Index ◽  
Extremal Graph ◽  
Graph Transformations ◽  
Bicyclic Graphs ◽  
Unified Method ◽  
Extremal Properties

The forgotten topological index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. In this paper, we characterize the extremal properties of the F-index (forgotten topological index). We first introduce some graph transformations which increase or decrease this index. Furthermore, we will determine the extremal acyclic, unicyclic and bicyclic graphs with minimum and maximum of the F-index by a unified method, respectively. Recently, Akhter et al. [S. Akhter, M. Imran and M. R. Farahani, Extremal unicyclic and bicyclic graphs with respect to the F-index, AKCE Int. J. Graphs Comb. 14 (2017) 80–91] characterized the extremal graph of unicyclic and bicyclic graphs with minimum of the F-index. We will provide a shorter proof.

Index Formula Index

1989 ◽  
Author(s):  
Rainer Bohrer ◽  
Helga Hartwig ◽  
Renate Jonuschat ◽  
Bernd Kalbskopf ◽  
Renate Nohl ◽  
...  
Keyword(s):  
Index Formula

scholarly journals The node cop‐win reliability of unicyclic and bicyclic graphs

Networks ◽  
2021 ◽  
Author(s):  
Maimoonah Ahmed ◽  
Ben Cameron
Keyword(s):  
Bicyclic Graphs

Developing an Outsourcing Partner Selection Model for Process with Two-Sided Specification Using Capability Index and Manufacturing Time Performance Index

2019 ◽  
Vol 26 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Kuen-Suan Chen ◽  
Tsang-Chuan Chang ◽  
Yun-Tsan Lin
Keyword(s):  
Performance Index ◽  
Business Models ◽  
Partner Selection ◽  
Selection Model ◽  
Index Formula ◽  
Time Performance ◽  
Capability Index ◽  
Point Estimates ◽  
Manufacturing Time

In the face of fierce global competition, firms are outsourcing important but nonessential tasks to external professional companies. Corporations are also turning from competitive business models to cooperative strategic partnerships in hopes of swiftly responding to consumer needs and enhancing overall efficiency and industry competitiveness. This research developed an outsourcing partner selection model in hopes of helping firms select better outsourcing partners for long-term collaborations. Process quality and manufacturing time are vital when evaluating outsourcing partner. We therefore used process capability index [Formula: see text] and manufacturing time performance index [Formula: see text] in the proposed model. Sample data from random samples are needed to calculate the point estimates of indices, however, it is impossible to obtain a sample with a structure completely identical to that of the population, which means that sampling generates unavoidable sampling errors. The reliability of point estimates are also uncertain, which inevitably leads to misjudgment in some cases. Thus, to reduce estimate errors and increase assessment reliability, we calculated the [Formula: see text]% confidence intervals of the indices [Formula: see text] and [Formula: see text], then constructed the joint confidence region of [Formula: see text] and [Formula: see text] to develop an outsourcing partner selection model that will help firms select better outsourcing partners for long-term collaborations. We also provide a case as an illustration of how the proposed selection model is implemented.

scholarly journals Permutation Matrices, Their Discrete Derivatives and Extremal Properties

2020 ◽  
Vol 48 (4) ◽  
pp. 719-740
Author(s):  
Richard A. Brualdi ◽  
Geir Dahl
Keyword(s):  
Permutation Matrix ◽  
Permutation Matrices ◽  
Discrete Derivative ◽  
The Relationship ◽  
Derivatives Of ◽  
Extremal Properties

AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

Extremal Properties of an Intermittent Poisson Process Generating 1/f Noise

2016 ◽  
Vol 15 (04) ◽  
pp. 1650028 ◽  
Author(s):  
Ferdinand Grüneis
Keyword(s):  
Stochastic Processes ◽  
Poisson Process ◽  
Total Power ◽  
Spectral Features ◽  
Active Period ◽  
Quiescent Period ◽  
The Family ◽  
Random Intervals ◽  
Theoretical Results ◽  
Extremal Properties

It is well-known that the total power of a signal exhibiting a pure [Formula: see text] shape is divergent. This phenomenon is also called the infrared catastrophe. Mandelbrot claims that the infrared catastrophe can be overcome by stochastic processes which alternate between active and quiescent states. We investigate an intermittent Poisson process (IPP) which belongs to the family of stochastic processes suggested by Mandelbrot. During the intermission [Formula: see text] (quiescent period) the signal is zero. The active period is divided into random intervals of mean length [Formula: see text] consisting of a fluctuating number of events; this is giving rise to so-called clusters. The advantage of our treatment is that the spectral features of the IPP can be derived analytically. Our considerations are focused on the case that intermission is only a small disturbance of the Poisson process, i.e., to the case that [Formula: see text]. This makes it difficult or even impossible to discriminate a spike train of such an IPP from that of a Poisson process. We investigate the conditions under which a [Formula: see text] spectrum can be observed. It is shown that [Formula: see text] noise generated by the IPP is accompanied with extreme variance. In agreement with the considerations of Mandelbrot, the IPP avoids the infrared catastrophe. Spectral analysis of the simulated IPP confirms our theoretical results. The IPP is a model for an almost random walk generating both white and [Formula: see text] noise and can be applied for an interpretation of [Formula: see text] noise in metallic resistors.

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