Combinatorics with Emphasis on the Theory of Graphs

1977 ◽  
Author(s):  
Jack E. Graver ◽  
Mark E. Watkins
Keyword(s):  
Theory Of Graphs

scholarly journals Probability Models for Assessing Effectiveness of Advertising Channels in the Internet Environment

2018 ◽  
pp. 209-215
Keyword(s):  
Graph Theory ◽  
Markov Chains ◽  
Markov Processes ◽  
The Internet ◽  
Probability Models ◽  
Method Of Calculation ◽  
Internet Environment ◽  
The Impact ◽  
Theory Of Graphs ◽  
Selection Of

Nowadays, marketing specialists simultaneously use several channels to attract visitors to websites. There is a difficulty in assessing not only the efficiency and conversion of each channel separately, but also in their interconnection. The problem occurs when users visit a website from several sources and only after that do the key action. To assess the effectiveness and selection of the most optimal channels, different models of attribution are used. The models are reviewed in the article. However, we propose to use multi-channel attribution, which provides an aggregate assessment of multi-channel sequences, taking into account that they are interdependent. The purpose of the paper is to create an attribution model that comprehensively evaluates multi-channel sequences and shows the effect of each channel on the conversion. The presented model of attribution can be based on the theory of graphs or Markov chains. The first method of calculation is more visual, the second (based on Markov chains) allows for work with a large amount of data. As a result, a model of multi-channel attribution was presented, which is based on Markov processes or graph theory. It allows for maximum comprehensive assessing of the impact of each channel on the conversion. On the basis of the two methods, calculations were carried out, confirming the adequacy of the model used for the tasks assigned.

Theory of Graphs

1977 ◽  
pp. 143-216
Author(s):  
Horst A. Eiselt ◽  
Helmut von Frajer
Keyword(s):  
Theory Of Graphs

Binomial incidence matrix of a semigraph

2020 ◽  
pp. 2150017
Author(s):  
Jyoti Shetty ◽  
G. Sudhakara
Keyword(s):  
Graph Theory ◽  
Complete Graph ◽  
Adjacency Matrix ◽  
Incidence Matrix ◽  
Systematic Approach ◽  
Line Graph ◽  
The Matrix ◽  
Theory Of Graphs

A semigraph, defined as a generalization of graph by  Sampathkumar, allows an edge to have more than two vertices. The idea of multiple vertices on edges gives rise to multiplicity in every concept in the theory of graphs when generalized to semigraphs. In this paper, we define a representing matrix of a semigraph [Formula: see text] and call it binomial incidence matrix of the semigraph [Formula: see text]. This matrix, which becomes the well-known incidence matrix when the semigraph is a graph, represents the semigraph uniquely, up to isomorphism. We characterize this matrix and derive some results on the rank of the matrix. We also show that a matrix derived from the binomial incidence matrix satisfies a result in graph theory which relates incidence matrix of a graph and adjacency matrix of its line graph. We extend the concept of “twin vertices” in the theory of graphs to semigraph theory, and characterize them. Finally, we derive a systematic approach to show that the binomial incidence matrix of any semigraph on [Formula: see text] vertices can be obtained from the incidence matrix of the complete graph [Formula: see text].

Mathematische Modelle für reaktionskinetische Phänomene

1969 ◽  
Vol 24 (4) ◽  
pp. 664-673 ◽  
Author(s):  
K. Heckmann ◽  
W. Vollmerhaus ◽  
J. Kutschera ◽  
E. Vollmerhaus
Keyword(s):  
Digital Computer ◽  
Essential Feature ◽  
Linear Equations ◽  
Algebraic Solution ◽  
Minimum Length ◽  
Theoretical Treatment ◽  
System Of Linear Equations ◽  
Special Model ◽  
Mathematische Modelle ◽  
Theory Of Graphs

Abstract The theoretical treatment of a number of stationary kinetic phenomena requires the solution of a system of linear equations. An algorithm is described which enables an algebraic solution to be found by means of a digital computer using probably a minimum length of calculation time. This algorithm is derived mainly from arguments based on the theory of graphs; its essential feature is the use of numerical operations on the indices of the coefficients of the equations. The algorithm is illustrated in terms of a special model of the membrane.

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