For connected graphs G with |V(G)| >= 4, Aut(G) ≅ Aut(C(G)) ≅ Aut(M(G)) as abstract groups, which yields new upper bounds on the distinguishing number and index of the central and middle graphs.
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Computes exact distinguishing chromatic numbers for middle graphs and equates distinguishing numbers for subdivision graphs to total distinguishing numbers.
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Automorphism groups and Distinguishing Colorings of Central and Middle Graphs
For connected graphs G with |V(G)| >= 4, Aut(G) ≅ Aut(C(G)) ≅ Aut(M(G)) as abstract groups, which yields new upper bounds on the distinguishing number and index of the central and middle graphs.
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Distinguishing chromatic number of middle and subdivision graphs
Computes exact distinguishing chromatic numbers for middle graphs and equates distinguishing numbers for subdivision graphs to total distinguishing numbers.