Hamming dimension of a graph-The case of Sierpiński graphs

Authors:
Sandi Klavar;Iztok Peterin;Sara Sabrina Zemljič
Affiliations:
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia and Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 M ...;Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ulica 17, 2000 Maribor, Slovenia;Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Venue:
European Journal of Combinatorics
Year:
2013

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Abstract

The Hamming dimension of a graph G is introduced as the largest dimension of a Hamming graph into which G embeds as an irredundant induced subgraph. An upper bound is proved for the Hamming dimension of Sierpinski graphs S"k^n, k=3. The Hamming dimension of S"3^n grows as 3^n^-^3. Several explicit embeddings are constructed along the way, in particular into products of generalized Sierpinski triangle graphs. The canonical isometric representation of Sierpinski graphs is also explicitly described.