﻿ Total domination in cubic Knodel graphs

# Total domination in cubic Knodel graphs

##### چکیده

A subset D of vertices of a graph G is a dominating set if for each u ∈ V (G) \ D, u is adjacent to somevertex v ∈ D. The domination number, γ(G) ofG, is the minimum cardinality of a dominating set of G. A setD ⊆ V (G) is a total dominating set if for eachu ∈ V (G), u is adjacent to some vertex v ∈ D. Thetotal domination number, γt (G) of G, is theminimum cardinality of a total dominating set of G. For an eveninteger \$nge 2\$ and \$1\le Delta \le lfloorlog_2nrfloor\$, aKnodel graph \$W_{Delta,n}\$ is a \$Delta\$-regularbipartite graph of even order n, with vertices (i,j), for\$i=1,2\$ and \$0le jle n/2-1\$, where for every \$j\$, \$0le jlen/2-1\$, there is an edge between vertex \$(1, j)\$ and every vertex\$(2,(j+2^k-1)\$ mod (n/2)), for \$k=0,1,cdots,Delta-1\$. In thispaper, we determine the total domination number in \$3\$-regularKnodel graphs \$W_{3,n}\$.

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عنوان ژورنال:

دوره 6  شماره 2

صفحات  221- 230

تاریخ انتشار 2021-12-01

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