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Displaying similar documents to “Value sets of graphs edge-weighted with elements of a finite abelian group”

Labeling the vertex amalgamation of graphs

Ramon M. Figueroa-Centeno, Rikio Ichishima, Francesc A. Muntaner-Batle (2003)

Discussiones Mathematicae Graph Theory

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A graph G of size q is graceful if there exists an injective function f:V(G)→ 0,1,...,q such that each edge uv of G is labeled |f(u)-f(v)| and the resulting edge labels are distinct. Also, a (p,q) graph G with q ≥ p is harmonious if there exists an injective function f : V ( G ) → Z q such that each edge uv of G is labeled f(u) + f(v) mod q and the resulting edge labels are distinct, whereas G is felicitous if there exists an injective function f : V ( G ) → Z q + 1 such that each edge uv of G is labeled f(u) + f(v) mod...

Median of a graph with respect to edges

A.P. Santhakumaran (2012)

Discussiones Mathematicae Graph Theory

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For any vertex v and any edge e in a non-trivial connected graph G, the distance sum d(v) of v is d ( v ) = ∑ u ∈ V d ( v , u ) , the vertex-to-edge distance sum d₁(v) of v is d ₁ ( v ) = ∑ e ∈ E d ( v , e ) , the edge-to-vertex distance sum d₂(e) of e is d ₂ ( e ) = ∑ v ∈ V d ( e , v ) and the edge-to-edge distance sum d₃(e) of e is d ₃ ( e ) = ∑ f ∈ E d ( e , f ) . The set M(G) of all vertices v for which d(v) is minimum is the median of G; the set M₁(G) of all vertices v for which d₁(v) is minimum is the vertex-to-edge median of G; the set M₂(G) of all edges e for which d₂(e) is minimum is the edge-to-vertex...

New edge neighborhood graphs

Ali A. Ali, Salar Y. Alsardary (1997)

Czechoslovak Mathematical Journal

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Let G be an undirected simple connected graph, and e = u v be an edge of G . Let N G ( e ) be the subgraph of G induced by the set of all vertices of G which are not incident to e but are adjacent to u or v . Let 𝒩 e be the class of all graphs H such that, for some graph G , N G ( e ) ≅ H for every edge e of G . Zelinka [3] studied edge neighborhood graphs and obtained some special graphs in 𝒩 e . Balasubramanian and Alsardary [1] obtained some other graphs in 𝒩 e . In this paper we given some new graphs in 𝒩 e .

On signed edge domination numbers of trees

Bohdan Zelinka (2002)

Mathematica Bohemica

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The signed edge domination number of a graph is an edge variant of the signed domination number. The closed neighbourhood N G [ e ] of an edge e in a graph G is the set consisting of e and of all edges having a common end vertex with e . Let f be a mapping of the edge set E ( G ) of G into the set { - 1 , 1 } . If ∑ x ∈ N [ e ] f ( x ) ≥ 1 for each e ∈ E ( G ) , then f is called a signed edge dominating function on G . The minimum of the values ∑ x ∈ E ( G ) f ( x ) , taken over all signed edge dominating function f on G , is called the signed edge domination number...

Graceful signed graphs

Mukti Acharya, Tarkeshwar Singh (2004)

Czechoslovak Mathematical Journal

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A ( p , q ) -sigraph S is an ordered pair ( G , s ) where G = ( V , E ) is a ( p , q ) -graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E + and E - consist of m positive and n negative edges of G , respectively, where m + n = q . Given positive integers k and d , S is said to be ( k , d ) -graceful if the vertices of G can be labeled with distinct integers from the set { 0 , 1 , ⋯ , k + ( q - 1 ) d } such that when each edge u v of G is assigned the product of its sign and the absolute difference of the integers assigned to...

Decomposition of complete graphs into ( 0 , 2 ) -prisms

Sylwia Cichacz, Soleh Dib, Dalibor Fronček (2014)

Czechoslovak Mathematical Journal

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R. Frucht and J. Gallian (1988) proved that bipartite prisms of order 2 n have an α -labeling, thus they decompose the complete graph K 6 n x + 1 for any positive integer x . We use a technique called the ρ + -labeling introduced by S. I. El-Zanati, C. Vanden Eynden, and N. Punnim (2001) to show that also some other families of 3-regular bipartite graphs of order 2 n called generalized prisms decompose the complete graph K 6 n x + 1 for any positive integer x .