A new lower bound for doubly metric dimension and related extremal differences

In this paper a new graph invariant based on the minimal hitting set problem is introduced. It is shown that it represents a tight lower bound for the doubly metric dimension of a graph. Exact values of new invariant for paths, stars, complete graphs and complete bipartite graph are obtained. The paper analyzes some tight bounds for the new invariant in general case. Also several extremal differences between some related invariants are determined

On some interconnections between combinatorial optimization and extremal graph theory

The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions

The traveling salesman problem: The spectral radius and the length of an optimal tour

We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs with distances between cities as edge weights. Computational experiments with randomly generated instances on 50 and 100 vertices with the uniform distribution of integer edge weights in interval [1, 100] show that there exists a correlation between the sequences of the spectral radii of the distance matrices and the lengths of optimal tours obtained by the well known TSP solver Concorde. In this paper we give a partial theoretical explanation of this correlation.Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles. Sciences mathématiques. . - 43 , 151 (2018

Three-stage entry game: The strategic effects of advertising

This paper analyzes the effects of investment in advertising in the three-stage entry game model with one incumbent and one potential entrant firm. It is shown that if a game theory is applied, under particular conditions, advertising can be used as a strategic weapon in the market entry game. Depending on the level of the advertising interaction factor, conditions for over-investment in advertising for strategic purposes are given. Furthermore, three specific cases are analyzed: strictly predatory advertising, informative advertising and the case when one firm’s advertising cannot directly influence the other firm's profit. For each of them, depending on the costs of advertising and marginal costs, equilibrium is determined, and conditions under which it is possible to deter the entry are given. It is shown that if the value of the advertising interaction factor increases, power of using advertising as a weapon to deter entry into the market decreases. Thus, in the case of informative advertising, advertising cannot be used as a tool for deterring entry into the market, while in the case of predatory advertising, it can. Also, we have proved that in the case of strictly informative advertising an over-investment never occurs, while in the two other cases, there is always over-investment either to deter or to accommodate the entry

Computing strong metric dimension of some special classes of graphs by genetic algorithms

In this paper we consider the NP-hard problem of determining the strong metric dimension of graphs. The problem is solved by a genetic algorithm that uses binary encoding and standard genetic operators adapted to the problem. This represents the first attempt to solve this problem heuristically. We report experimental results for the two special classes of ORLIB test instances: crew scheduling and graph coloring

Computing the metric dimension of graphs by genetic algorithms

Graph theory, Metric dimension, Evolutionary approach,