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On smallest regular graphs with a given isopart
Author(s) -
Fink John Frederick
Publication year - 1985
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190090108
Subject(s) - mathematics , combinatorics , graph , degree (music) , integer (computer science) , discrete mathematics , order (exchange) , strongly regular graph , pathwidth , line graph , computer science , physics , acoustics , programming language , finance , economics
For a nonempty graph, G, we define p(G) and r(G) to be respectively the minimum order and minimum degree of regularity among all connected regular graphs H having a nontrivial decomposition into subgraphs isomorphic to G. By f(G), we denote the least integer t for which there is a connected regular graph H having a decomposition into t subgraphs isomorphic to G. In this article, the values of these parameters are determined for complete graphs, cycles, and stars. Furthermore, we show that Δ( T ) ⩽ r ( T ) ⩽ δ ( T ) + 1 for every tree T . and r ( T ) Δ( T ) if the maximum degree Δ( T ) is even.