On super edge magic deficiency of kite graphs. (Q2864449)

For a graph \(G(V,E)\) with \(p\) vertices and \(q\) edges, a bijection \(\phi : V\cup E\to \{1,2,\dots ,p+q\}\), where \(\phi (V)=\{1,2,\dots ,p\}\), is called a super edge magic labeling if for every \(xy\in E\) the sum \(f(x)+f(y)+f(xy)\) is equal to the same constant. The super edge magic deficiency of a graph \(G\), \(\mu _s(G)\), is the minimum number \(m\) such that the graph \(G\cup mK_1\) admits a super edge magic labeling (or \(\mu _s(G)=\infty \), if no such \(m\) exists).NEWLINENEWLINEAn \((n,t)\)-kite is a graph consisting of the cycle \(C_n\) with a path of length \(t\) attached to one of the vertices of the cycle. It is proved that when \(G\) is an \((n,t)\)-kite, \(n\) is odd, \(n\geq 5\), \(t\) is even and \(t\geq 4\), then \(\mu _s(G)=1\). It is further proved that when \(n\) is odd, \(n\geq 5\), and \(t\geq 7,~t\neq 11,~t\equiv 3\pmod 4\), then \(\mu _s(G)\leq 1\). Finally, it is proved that if \(n\geq 10, ~n\equiv 2\pmod 4\) and \(4\leq t\leq 5\), then \(\mu _s(G)\leq 1\). The results complement unpublished results by Ahmad and Muntaner-Batle for \(n\) odd and \(t\equiv 0,1\pmod 4\).