An injective function f : V pGq Ñ t0, 1, 2, . . . , qu is an odd sum labeling if the induced edge labeling f defined by f puvq fpuq fpvq, for all uv P EpGq, is bijective and f pEpGqq t1, 3, 5, . . . , 2q 1u. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper we study the odd sum property of graphs obtained by duplicating any edge of some graphs.

let g=(v,e) be a simple graph. an edge labeling f:e to {0,1} induces a vertex labeling f^+:v to z_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(1)-v_f(0) is called the edge-f...

‎‎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(...

An edge magic total labeling of a graph with p vertices and q edges is a bijection from the set of vertices and edges to 1, 2, . . . , p+ q such that for every edge the sums of the label of the edge and the label of its two end vertices are constant. Otherwise if the sum is distinct, it is said to be an edge-antimagic total labeling. A graph is called edgeantimagic if it admits edge-antimagic t...

An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is local antimagic if vertex-weights are distinct for pair neighboring vertices, where vertex-weight sum labels all edges incident with that vertex. Any induces proper vertex coloring G color its vertex-weight. This naturally leads to concept chromatic number. The number defined be minimum colors take...

We propose a new puzzle: Label the eight vertices of cube using distinct integers between 0 and 12 (both inclusive) such that induced labeling each edge, given by sum labels its end points, causes edges to be labeled with odd numbers 1, 3, … 23. Any solution puzzle is called super odd-sum labeling. deftly discover all cube.

A graph G of order p and size q is edge-magic if there is a bijective function f : V (G) ∪ E(G) −→ {i} i=1 such that f(x) + f(xy) + f(y) = k, for all xy ∈ E(G). The function f is an edge-magic labeling of G and the sum k is called either the magic sum, the valence or the weight of f . Furthermore, if f(V (G)) = {i}pi=1 then f is a super edge-magic labeling of G. In this paper we study the valen...

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . . , |V (G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total label...