A SURVEY AND SELECTED RESULTS ON INVERSE DOMINATION IN GRAPHS

Authors

  • M. H. Muddebihal Department of mathematics, Gulbarga University,Gulbarga –585102, Karnataka, INDIA.
  • Vedula Padmavathi Department of mathematics, A. G. Patil Institute of Technology, Solapur, Maharashtra, INDIA

Keywords:

Domination, Inverse domination.

Abstract

Historically, The concept of domination in graphsfound its origin in 1850s with the interest of several chess players. Among the numerous applications of the domination theory in graphs, the most often discussed is a communication network. This network consists of communication links between a fixed set of sites. The problem is to select a smallest set of sites at which the transmitters are placed so thatevery other site in the network is joined by a direct communication link to the site, which has a transmitter. In other words the problem is to find a minimum dominating set in the graph corresponding to this network.Kulli and Sigarkanti[13]considered the problem of selecting two disjoint sets of transmitting stations so that one set can provide service in the case of failure of some of the transmitting stations of the other set. This led them to define the inverse domination number .Let Dbe a -set of G. If is another-set of Gthenis called an inverse dominating set with respect to D.

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Published

2021-03-27

Issue

2016: NITET

Section

Articles

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