Unmixed r-partite graphs
Reza Jafarpoure Golzari, Rashid Zaare-Nahandi
TL;DR
This paper extends the characterization of unmixed bipartite graphs to unmixed r-partite graphs under a specific condition, generalizing Villarreal's theorem and providing illustrative examples and counterexamples.
Contribution
It introduces a new characterization of unmixed r-partite graphs that generalizes existing bipartite graph results, with additional examples and counterexamples.
Findings
Established a new characterization for unmixed r-partite graphs.
Generalized Villarreal's theorem from bipartite to r-partite graphs.
Provided relevant examples and counterexamples.
Abstract
Unmixed bipartite graphs have been characterized by Ravadra and Villarreal independently. Our aim in this paper is to characterize unmixed r-partite graphs under a certain condition, witch is a generalization of villarreal's theorem on bipartite graphs. Also we give some examples and counterexamples in relevance this subject.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Advanced Graph Theory Research