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- W2207396906 abstract "Abstract: Root and root finding are concepts familiar to mostbranches of mathematics.In graph theory, H is a square root of Gand G is the square of H iftwo vertices x,y have an edge in G if and only ifx,y are of distance at most two in H.Graph square is a basic operationwith a number of results about its properties in the literature.We study the characterizationand recognition problems of graph powers. There are algorithmic and computational approaches to answer thedecision problem of whether a given graph is a certain power of any graph.There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four.The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs withgirth 5 is NP-complete.This result is providing the complete dichotomy theorem for square root finding problem." @default.
- W2207396906 created "2016-06-24" @default.
- W2207396906 creator A5076818140 @default.
- W2207396906 date "2013-01-24" @default.
- W2207396906 modified "2023-09-28" @default.
- W2207396906 title "Square Root Finding In Graphs" @default.
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