scholarly journals On the price of stability of some simple graph-based hedonic games

2020 ◽  
Author(s):  
Christos Kaklamanis ◽  
Panagiotis Kanellopoulos ◽  
Konstantinos Papaioannou ◽  
Dimitris Patouchas
Keyword(s):  
Simple Graph ◽  
Price Of Stability ◽  
Hedonic Games

The Price of Stability of Simple Symmetric Fractional Hedonic Games

2016 ◽  
pp. 220-232 ◽  
Author(s):  
Christos Kaklamanis ◽  
Panagiotis Kanellopoulos ◽  
Konstantinos Papaioannou
Keyword(s):  
Price Of Stability ◽  
Hedonic Games

scholarly journals Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

2018 ◽  
Vol 62 ◽  
pp. 315-371 ◽  
Author(s):  
Vittorio Bilò ◽  
Angelo Fanelli ◽  
Michele Flammini ◽  
Gianpiero Monaco ◽  
Luca Moscardelli
Keyword(s):  
Social Welfare ◽  
Optimal Solution ◽  
Solution Concept ◽  
Coalition Structure ◽  
Upper And Lower Bounds ◽  
Price Of Stability ◽  
Average Value ◽  
Tree Graphs ◽  
Hedonic Games ◽  
Stable Outcome

We consider fractional hedonic games, a subclass of coalition formation games that can be succinctly modeled by means of a graph in which nodes represent agents and edge weights the degree of preference of the corresponding endpoints. The happiness or utility of an agent for being in a coalition is the average value she ascribes to its members. We adopt Nash stable outcomes as the target solution concept; that is we focus on states in which no agent can improve her utility by unilaterally changing her own group. We provide existence, efficiency and complexity results for games played on both general and specific graph topologies. As to the efficiency results, we mainly study the quality of the best Nash stable outcome and refer to the ratio between the social welfare of an optimal coalition structure and the one of such an equilibrium as to the price of stability. In this respect, we remark that a best Nash stable outcome has a natural meaning of stability, since it is the optimal solution among the ones which can be accepted by selfish agents. We provide upper and lower bounds on the price of stability for different topologies, both in case of weighted and unweighted edges. Beside the results for general graphs, we give refined bounds for various specific cases, such as triangle-free, bipartite graphs and tree graphs. For these families, we also show how to efficiently compute Nash stable outcomes with provable good social welfare.

scholarly journals Additively Separable Hedonic Games with Social Context

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 71
Author(s):  
Gianpiero Monaco ◽  
Luca Moscardelli ◽  
Yllka Velaj
Keyword(s):  
Nash Equilibrium ◽  
Social Context ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Strategic Interaction ◽  
Price Of Stability ◽  
Fundamental Class ◽  
New Model ◽  
Hedonic Games ◽  
And Performance

In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

scholarly journals Power graphs and exchange property for resolving sets

2019 ◽  
Vol 17 (1) ◽  
pp. 1303-1309 ◽  
Author(s):  
Ghulam Abbas ◽  
Usman Ali ◽  
Mobeen Munir ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Shin Min Kang
Keyword(s):  
Present Article ◽  
Linear Algebra ◽  
Finite Groups ◽  
Robot Navigation ◽  
Simple Graph ◽  
Exchange Property ◽  
Metric Dimension ◽  
Sufficient Condition ◽  
Resolving Set ◽  
Dihedral Groups

Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given. A sufficient condition for the graph to have the exchange property for resolving sets is found. Consequently, every minimal resolving set in the graph forms a basis for a matriod in the context of independence defined by Boutin [Determining sets, resolving set and the exchange property, Graphs Combin., 2009, 25, 789-806]. Also, a new way to define a matroid on finite ground is deduced. It is proved that the matroid is strongly base orderable and hence satisfies the conjecture of White [An unique exchange property for bases, Linear Algebra Appl., 1980, 31, 81-91]. As an application, it is shown that the power graphs of some finite groups can define a matroid. Moreover, we also compute the metric dimension of the power graphs of dihedral groups.

scholarly journals The Irregularity and Modular Irregularity Strength of Fan Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 605
Author(s):  
Martin Bača ◽  
Zuzana Kimáková ◽  
Marcela Lascsáková ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Isolated Vertex ◽  
Positive Integers ◽  
Irregularity Strength

For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G)→{1,2,…,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wtφ(v)=∑u∈N(v)φ(uv), are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.

scholarly journals k-Zumkeller labeling of super subdivision of some graphs

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
M. Basher
Keyword(s):  
Simple Graph ◽  
Natural Numbers ◽  
Injective Function ◽  
Planar Grid ◽  
Circular Ladder

AbstractA simple graph $$G=(V,E)$$ G = ( V , E ) is said to be k-Zumkeller graph if there is an injective function f from the vertices of G to the natural numbers N such that when each edge $$xy\in E$$ x y ∈ E is assigned the label f(x)f(y), the resulting edge labels are k distinct Zumkeller numbers. In this paper, we show that the super subdivision of path, cycle, comb, ladder, crown, circular ladder, planar grid and prism are k-Zumkeller graphs.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

scholarly journals The Synergistic Effects of Alloying on the Performance and Stability of Co3Mo and Co7Mo6 for the Electrocatalytic Hydrogen Evolution Reaction

Hydrogen ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 11-21
Author(s):  
Youyi Sun ◽  
Alexey Y. Ganin
Keyword(s):  
Hydrogen Evolution ◽  
Synergistic Effects ◽  
Alkaline Media ◽  
Price Of Stability ◽  
X Ray Diffraction ◽  
Free Standing ◽  
X Ray ◽  
Current Decay ◽  
Earth Abundant ◽  
Current Densities

Metal alloys have become a ubiquitous choice as catalysts for electrochemical hydrogen evolution in alkaline media. However, scarce and expensive Pt remains the key electrocatalyst in acidic electrolytes, making the search for earth-abundant and cheaper alternatives important. Herein, we present a facile and efficient synthetic route towards polycrystalline Co3Mo and Co7Mo6 alloys. The single-phased nature of the alloys is confirmed by X-ray diffraction and electron microscopy. When electrochemically tested, they achieve competitively low overpotentials of 115 mV (Co3Mo) and 160 mV (Co7Mo6) at 10 mA cm−2 in 0.5 M H2SO4, and 120 mV (Co3Mo) and 160 mV (Co7Mo6) at 10 mA cm−2 in 1 M KOH. Both alloys outperform Co and Mo metals, which showed significantly higher overpotentials and lower current densities when tested under identical conditions, confirming the synergistic effect of the alloying. However, the low overpotential in Co3Mo comes at the price of stability. It rapidly becomes inactive when tested under applied potential bias. On the other hand, Co7Mo6 retains the current density over time without evidence of current decay. The findings demonstrate that even in free-standing form and without nanostructuring, polycrystalline bimetallic electrocatalysts could challenge the dominance of Pt in acidic media if ways for improving their stability were found.

ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES

2021 ◽  
pp. 1-5
Author(s):  
SH. RAHIMI ◽  
Z. AKHLAGHI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Regular Graph ◽  
Simple Graph ◽  
Conjugacy Classes ◽  
A Finite Group

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

scholarly journals A Comparison of Genetic Representations and Initialisation Methods for the Multi-objective Shortest Path Problem on Multigraphs

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Lilla Beke ◽  
Michal Weiszer ◽  
Jun Chen
Keyword(s):  
Shortest Path ◽  
Time Budget ◽  
Exact Algorithm ◽  
Simple Graph ◽  
Shortest Path Problem ◽  
Future Application ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Problem Instances

AbstractThis paper compares different solution approaches for the multi-objective shortest path problem (MSPP) on multigraphs. Multigraphs as a modelling tool are able to capture different available trade-offs between objectives for a given section of a route. For this reason, they are increasingly popular in modelling transportation problems with multiple conflicting objectives (e.g., travel time and fuel consumption), such as time-dependent vehicle routing, multi-modal transportation planning, energy-efficient driving, and airport operations. The multigraph MSPP is more complex than the NP-hard simple graph MSPP. Therefore, approximate solution methods are often needed to find a good approximation of the true Pareto front in a given time budget. Evolutionary algorithms have been successfully applied for the simple graph MSPP. However, there has been limited investigation of their applications to the multigraph MSPP. Here, we extend the most popular genetic representations to the multigraph case and compare the achieved solution qualities. Two heuristic initialisation methods are also considered to improve the convergence properties of the algorithms. The comparison is based on a diverse set of problem instances, including both bi-objective and triple objective problems. We found that the metaheuristic approach with heuristic initialisation provides good solutions in shorter running times compared to an exact algorithm. The representations were all found to be competitive. The results are encouraging for future application to the time-constrained multigraph MSPP.

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