Geodesic
Graph homomorphisms and components of quotient graphs
Bubboloni, Daniela1 
1 Università degli Studi di Firenze, Italy
Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 39-60

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We study how the number c(X) of components of a graph X can be expressed through the number and properties of the components of a quotient graph X/∼. We partially rely on classic qualifications of graph homomorphisms such as locally constrained homomorphisms and on the concept of equitable partition and orbit partition. We introduce the new definitions of pseudo-covering homomorphism and of component equitable partition, exhibiting interesting inclusions among the various classes of considered homomorphisms. As a consequence, we find a procedure for computing c(X) when the projection on the quotient X/∼ is pseudo-covering. That procedure becomes particularly easy to handle when the partition corresponding to X/∼ is an orbit partition.

Publié le :
DOI : 10.4171/RSMUP/138-2
Classification : 05
Mots-clés : Graph homomorphism, quotient graph, components, power graphs

Bubboloni, Daniela 1

1 Università degli Studi di Firenze, Italy 
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     title = {Graph homomorphisms and components of quotient graphs},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {39--60},
     publisher = {European Mathematical Society Publishing House},
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Bubboloni, Daniela. Graph homomorphisms and components of quotient graphs. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 39-60. doi: 10.4171/RSMUP/138-2

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