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Induced Graphoidal Covers In A Graph

Authors: K. Ratan Singh; P. K. Das;

Induced Graphoidal Covers In A Graph

Abstract

{"references": ["B. D. Acharya, E. Sampathkumar, Graphoidal covers and graphoidal\ncovering number of a graph, Indian J. Pure Appl. Math., 18 (10) (1987)\npp 882-890.", "S. Arumugam, S, Hamid, Simple graphoidal covers in a graph, J. Comb.\nMath. Comb. Comput., 64 (2008) pp 79-95 .", "S. Arumugam, B. D. Acharya, E. Sampathkumar, Graphoidal covers of\na graph: a creative review, in Proc. National Workshop on Graph Theory\nand its applications, Manonmaniam Sundaranar University, Tirunelveli,\nTata McGraw-Hill, New Delhi, pp 1-28, 1997.", "S. Arumugam, Path covers in graphs, Lecture Notes of the National\nWorkshop on Decompositions of Graphs and Product Graphs held at\nAnnamalai University, Tamil Nadu, during January 3-7, 2006.", "F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.", "K. Ratan Singh, P. K. Das, On Graphoidal covers of bicyclic graphs,\n(submitted for publication)."]}

An induced graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced cycle or an induced path. The minimum cardinality of an induced graphoidal cover of G is called the induced graphoidal covering number of G and is denoted by ηi(G) or ηi. Here we find induced graphoidal cover for some classes of graphs.

Keywords

Induced graphoidal cover, Induced graphoidal covering number., Graphoidal cover

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