A New Address on Classical Average Assignment of Various Graphs Obtained from Cycle

A New Address on Classical Average Assignment of Various Graphs Obtained From Cycle

A.     Rajesh Kannan

Department of Mathematics

Mepco Schlenk Engineering College, Sivakasi-626 005, Tamil Nadu, India

Email: rajmaths@gmail.com

Abstract

A function is called a classical average assignment of a graph  with  vertices and edges if  is injective and the induced function defined by the flooring function of the average of root square, harmonic,
geometric and arithmetic means of the vertex labels of the end vertices of each
edge,  is bijective.  A graph that admits a classical average assignment is called an classical average assignment graph.  Here,  we have discussed the classical average assignment of a cycle, the graph obtained from a path by replacing any of its edges by a cycle, the triangular snake, the alternate triangular snake, the quadrilateral snake, the alternate quadrilateral snake, the tadpoles, the graph  and the  triangular ladder graph.

Key words:   Labeling, cycle graph, classical average assignment, classical average assignment graph, identifying an edge.