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Game total domination subdivision number of a graph

Authors: Seyed Mahmoud Sheikholeslami; Jafar Amjadi; Hossein Karami;

Game total domination subdivision number of a graph

Abstract

A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination numberγt(G) is the minimum cardinality of a total dominating set of G. The game total domination subdivision number of a graph G is defined by the following game. Two players 𝒟 and 𝒜, 𝒟 playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided. The game ends when all the edges of G are marked or subdivided and results in a new graph G′. The purpose of 𝒟 is to minimize the total domination number γt(G′) of G′ while 𝒜 tries to maximize it. If both 𝒜 and 𝒟 play according to their optimal strategies, γt(G′) is well defined. We call this number the game total domination subdivision number of G and denote it by γgt(G). In this paper we initiate the study of the game total domination subdivision number of a graph and present some (sharp) bounds for this parameter.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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