The Cycle Discrepancy of Three-Regular Graphs |
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| Authors: | Sarmad Abbasi Laeeq Aslam |
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| Institution: | 1. 117-BB, Phase IV, DHA, Lahore, Pakistan
2. Punjab University College of Information Technology, University of the Punjab, Lahore, Pakistan
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| Abstract: | Let G = (V, E) be an undirected graph and C(G){{\mathcal C}(G)} denote the set of all cycles in G. We introduce a graph invariant cycle discrepancy, which we define as
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${\rm cycdisc}(G) = \min_{\chi: V \mapsto \{+1, -1\}}
\max_{ C \in {\mathcal C} (G)}
\left|\sum_{v \in C}
\chi(v)\right|.${\rm cycdisc}(G) = \min_{\chi: V \mapsto \{+1, -1\}}
\max_{ C \in {\mathcal C} (G)}
\left|\sum_{v \in C}
\chi(v)\right|. |
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| Keywords: | |
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