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