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   coalition of cubic graphs of order at most 10  
   
نویسنده alikhani saeid ,golmohammadi hamidreza ,konstantinova elena v.
منبع communications in combinatorics and optimization - 2024 - دوره : 9 - شماره : 3 - صفحه:437 -450
چکیده    The coalition in a graph g-consists of two disjoint sets of vertices $v_{1}$ and $v_{2}$, neither of which is a dominating set but whose union $v_{1}cup  v_{2}, is a dominating set. a coalition partition in a graph $g$ is a vertex partition $pi$ = ${v_1, v_2,dots, v_k }$ such that every set $v_i in pi$ is not a dominating set but forms a coalition with another set $v_jin pi$ which is not a dominating set. the coalition number $c(g)$ equals the maximum $k$ of a coalition partition  of $g$. in this paper, we compute the coalition numbers of all cubic graphs of order at most $10$.
کلیدواژه coalition ,cubic graphs ,petersen graph
آدرس yazd university, department of mathematics, iran, novosibirsk state university, russia. sobolev institute of mathematics, russia, novosibirsk state university, russia. sobolev institute of mathematics, russia
پست الکترونیکی e_konsta@math.nsc.ru
 
     
   
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