\(k\)-Odd Edge Mean Labeling of Some Basic Graphs

K. Amuthavalli, S. Dineshkumar

Abstract


A \(\left(p,q\right)\) graph \(G\) is said to have a \(k\)-odd edge mean labeling \((k\ge 1)\), if there exists an injection \(f\) from the edges of \(G\) to \(\{0,1,2,3,\ldots,2k+2p-3\}\) such that the induced map \(f^*\) defined on \(V\) by \(f^{*} (v)=\left\lceil \frac{\sum f(vu) }{\deg (v)} \right\rceil\) is a bijection from \(V\) to \(\{2k-1,2k+1,2k+3,\ldots, 2k+2p-3\}\). A graph that admits a \(k\)-odd edge mean labeling is called a \(k\)-odd edge mean graph. In this paper, we have introduced \(k\)-odd edge mean labeling and we have investigated the same labeling for basic graphs like path and star.  Also we have examined the existence and non existence of cycles.

Keywords


\(k\)-Odd edge mean labeling; \(k\)-Odd edge mean graph

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.1012

eISSN 0975-5748; pISSN 0974-875X