### Abstract

A vertex v in a graph G=(V,X) is said to be weak if d(v)≤d(u) for every u adjacent to v in G. A set S ⊆ V is said to be weak if every vertex in S is a weak vertex in G. A weak set which is independent is called a weak independent set (WIS). The weak independence number wβ0(G) is the maximum cardinality of a WIS. We proved that wβ0(G)≤ p-δ. This bound is further refined in this paper and we characterize the graphs for which the new bound is attained.

Original language | English |
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Title of host publication | Proceedings of the World Congress on Engineering 2013, WCE 2013 |

Pages | 208-210 |

Number of pages | 3 |

Volume | 1 LNECS |

Publication status | Published - 25-11-2013 |

Event | 2013 World Congress on Engineering, WCE 2013 - London, United Kingdom Duration: 03-07-2013 → 05-07-2013 |

### Conference

Conference | 2013 World Congress on Engineering, WCE 2013 |
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Country | United Kingdom |

City | London |

Period | 03-07-13 → 05-07-13 |

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)

## Cite this

Bhat, R. S., Kamath, S. S., & Surekha (2013). An improved bound on weak independence number of a graph. In

*Proceedings of the World Congress on Engineering 2013, WCE 2013*(Vol. 1 LNECS, pp. 208-210)