A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

Acharya and Hegde have introduced the notion of strongly k-indexable graphs: A (p, q)-graph G is said to be strongly k-indexable if its vertices can be assigned distinct integers 0, 1, 2, ..., p − 1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices can be arranged as an arithmetic progression k, k+ 1, k + 2, ..., k + (q − 1). Such an assignment ...

Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent t...

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

A vertex magic total (VMT) labeling of a graph G = (V,E) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪E → {1, 2, . . . , |V | + |E|} so that for every x ∈ V , w(x) = λ(x)+ ∑ xy∈E λ(xy) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest possible integers, 1, 2, . . . , |V |. In thi...

A graph G is called super edge-magic if there exists a bijective function f : V (G) ∪ E (G) → {1, 2, . . . , |V (G)|+ |E (G)|} such that f (V (G)) = {1, 2, . . . , |V (G)|} and f (u) + f (v) + f (uv) is a constant for each uv ∈ E (G). A graph G with isolated vertices is called pseudo super edge-magic if there exists a bijective function f : V (G) → {1, 2, . . . , |V (G)|} such that the set {f (...