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S Monikandan
Manonmaniam Sundaranar University Tirunelveli -627012 Tamilnadu INDIA
Mathematics

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Nonsplit Graphs with Split Maximal Induced Subgraphs S Monikandan; V Manikandan
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 2 (JULY 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.2.988.217-234

Abstract

A split graph is a graph in which the vertices can be partitioned into an independent set and a clique. A graph is split if and only if it has no induced subgraph isomorphic to C5, C4 or 2K2, which is a well-known characterization for split graph. A property of a graph G is recognizable if it can be recognized from the collection of all maximal proper induced subgraphs of G. We show that any nonsplit graph can have at most five split maximal induced subgraphs. Also we list out all C5-free nonsplit graphs having split maximal induced subgraphs, which is the main and, in fact, tedious result of this paper
Co-Authors V Manikandan