A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

This paper extends the scenario of the Four Color Theorem in the following way. LetHd,k be the set of all k-uniform hypergraphs that can be (linearly) embedded into Rd . We investigate lower and upper bounds on the maximum (weak and strong) chromatic number of hypergraphs in Hd,k. For example, we can prove that for d ≥ 3 there are hypergraphs inH2d−3,d on n vertices whose weak chromatic number ...

In the definition of the graph parameters μ(G) and ν(G), introduced by Colin de Verdière, and in the definition of the graph parameter ξ(G), introduced by Barioli, Fallat, and Hogben, a transversality condition is used, called the Strong Arnol’d Hypothesis. In this paper, we define the Strong Arnol’d Hypothesis for linear subspaces L ⊆ R with respect to a graph G = (V,E), with V = {1, 2, . . . ...

Unextendible product bases (UPBs) play a key role in the study of quantum entanglement and nonlocality. Here we provide an equivalent characterization UPBs graph-theoretic terms. Different from previous investigations UPBs, which focused mostly on orthogonality relations between different states, our includes reformulation unextendibility condition. Building this characterization, develop const...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...

A (p, q) connected graph is edge-odd graceful graph if there exists an injective map f: E(G) → {1, 3, ..., 2q-1} so that induced map f+: V(G) → {0, 1,2, 3, ..., (2k-1)}defined by f+(x)  f(x, y) (mod 2k), where the vertex x is incident with other vertex y and k = max {p, q} makes all the edges distinct and odd. In this article, the Edgeodd gracefulness of strong product of P2 and Cn is obtaine...