A vertex magic total labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers with the property that the sum of the label on the vertex and the labels of its incident edges is a constant, independent of the choice of the vertex. A graph with vertex magic total labeling with two constants or is called a vertex bimagic total labeling. The...

‎‎let $g=(v,e)$ be a simple graph‎. ‎an edge labeling $f:eto {0,1}$ induces a vertex labeling $f^+:vtoz_2$ defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$‎, ‎where $z_2={0,1}$ is the additive group of order 2‎. ‎for $iin{0,1}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎a labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|le 1$‎. ‎$i_f(g)=v_f(...

In this paper we introduce a new type of labeling known as even vertex odd mean labeling. A graph G with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f : V (G) → {0, 2, 4, . . . , 2q−2, 2q} such that the induced map f∗ : E(G) → {1, 3, 5, . . . , 2q− 1} defined by f∗(uv) = f(u)+f(v) 2 is a bijection. A graph that admits an even ver...

For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...

For each positive integer \(k\), a simple graph \(G\) of order \(p\) is said to be \(k\)-prime labeling if there exists an injective function \(f\) whose labels are from \(k\) \(k+p-1\) that induces \(f^{+}:E(G)\to N\) the edges defined by \(f^{+}(uv)=\gcd(f(u),f(v))\), \(\forall\) \(e=uv \in E(G)\) such every pair neighbouring vertices relatively prime. This type known as graph. In this paper,...