Graphic sequences and split graphs

2016 ◽  
Vol 32 (4) ◽  
pp. 1005-1014
Author(s):  
Jian-hua Yin ◽  
Lei Meng ◽  
Meng-Xiao Yin
Keyword(s):  
Split Graphs

Split graphs

2021 ◽  
pp. 189-206
Author(s):  
Karen L. Collins ◽  
Ann N. Trenk
Keyword(s):  
Split Graphs

scholarly journals The Evolution of Networks and Local Public Good Provision: A Potential Approach

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 55
Author(s):  
Markus Kinateder ◽  
Luca Paolo Merlino
Keyword(s):  
Public Good ◽  
Nash Equilibria ◽  
Potential Game ◽  
Public Good Provision ◽  
Local Public Good ◽  
Steady State Distribution ◽  
State Distribution ◽  
Long Run ◽  
Split Graphs ◽  
Good Provision

In this paper, we propose a game in which each player decides with whom to establish a costly connection and how much local public good is provided when benefits are shared among neighbors. We show that, when agents are homogeneous, Nash equilibrium networks are nested split graphs. Additionally, we show that the game is a potential game, even when we introduce heterogeneity along several dimensions. Using this result, we introduce stochastic best reply dynamics and show that this admits a unique and stationary steady state distribution expressed in terms of the potential function of the game. Hence, even if the set of Nash equilibria is potentially very large, the long run predictions are sharp.

On class 2 split graphs

2010 ◽  
Vol 39 (17) ◽  
Author(s):  
Sheila de Almeida ◽  
Celia de Mello ◽  
Aurora Morgana
Keyword(s):  
Split Graphs

Three-rainbow coloring of split graphs

2015 ◽  
Vol 21 (3) ◽  
pp. 284-287
Author(s):  
Yumei Hu ◽  
Tingting Liu
Keyword(s):  
Split Graphs ◽  
Rainbow Coloring

scholarly journals Linear recognition of pseudo-split graphs

1994 ◽  
Vol 52 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Frédéric Maffray ◽  
Myriam Preissmann
Keyword(s):  
Split Graphs

scholarly journals Uniquely List Colorability of Complete Split Graphs

2021 ◽  
Vol 8 (1) ◽  
pp. 120-124
Author(s):  
Xuan Hung Xuan Hung
Keyword(s):  
Split Graphs

scholarly journals Study of Identifying Code Polyhedra for Some Families of Split Graphs

2014 ◽  
pp. 13-25 ◽  
Author(s):  
Gabriela Argiroffo ◽  
Silvia Bianchi ◽  
Annegret Wagler
Keyword(s):  
Identifying Code ◽  
Split Graphs

scholarly journals Vulnerability of super connected split graphs and bisplit graphs

2019 ◽  
Vol 12 (4-5) ◽  
pp. 1179-1185
Author(s):  
Litao Guo ◽  
◽  
Bernard L. S. Lin ◽  
Keyword(s):  
Split Graphs

scholarly journals An efficientg-centroid location algorithm for cographs

2005 ◽  
Vol 2005 (9) ◽  
pp. 1405-1413 ◽  
Author(s):  
V. Prakash
Keyword(s):  
Location Problem ◽  
Maximum Clique ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Outerplanar Graphs ◽  
Arbitrary Graph ◽  
Maximal Outerplanar Graphs ◽  
Split Graphs ◽  
Location Algorithm ◽  
Centroid Location

In 1998, Pandu Rangan et al. Proved that locating theg-centroid for an arbitrary graph is𝒩𝒫-hard by reducing the problem of finding the maximum clique size of a graph to theg-centroid location problem. They have also given an efficient polynomial time algorithm for locating theg-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present anO(nm)time algorithm for locating theg-centroid for cographs, wherenis the number of vertices andmis the number of edges of the graph.

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