IJFANS International Journal of Food and Nutritional Sciences

ISSN PRINT 2319 1775 Online 2320-7876

THE TOTAL EDGE FIXING EDGE-TO-EDGE GEODETIC NUMBER OF A GRAPH

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L.Merlin Sheela,M. Antony,

Abstract

In this article, we introduce the concept of the total edge fixing edge-to-edge geodetic number ????????????????????????(????)for an edge ????of a graph ????. The total edge fixing edge-to-edge geodetic number of certain classes of graphs including path, cycles, trees, complete graphs are studied. Also it is shown that for every pair of positive integers with 2 ≤ ???? ≤ ????, there exists a graph ???? such that ????????????????(????) = ???? and ????????????????????????(????) = ????,for some edge ????????(????).

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