Displaying similar documents to “Decomposition of complete graphs into ( 0 , 2 ) -prisms”

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...

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...

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 .

Rotation and jump distances between graphs

Gary Chartrand, Heather Gavlas, Héctor Hevia, Mark A. Johnson (1997)

Discussiones Mathematicae Graph Theory

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A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v, and w such that uv ∈ E(G), uw ∉ E(G), and H = G-uv+uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u,v,w, and x such that uv ∈ E(G), wx∉ E(G), and H = G-uv+wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. It is shown that for every two graphs G and H of the same order (at least...

On the minus domination number of graphs

Hailong Liu, Liang Sun (2004)

Czechoslovak Mathematical Journal

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Let G = ( V , E ) be a simple graph. A 3 -valued function f V ( G ) → { - 1 , 0 , 1 } is said to be a minus dominating function if for every vertex v ∈ V , f ( N [ v ] ) = ∑ u ∈ N [ v ] f ( u ) ≥ 1 , where N [ v ] is the closed neighborhood of v . The weight of a minus dominating function f on G is f ( V ) = ∑ v ∈ V f ( v ) . The minus domination number of a graph G , denoted by γ - ( G ) , equals the minimum weight of a minus dominating function on G . In this paper, the following two results are obtained. (1) If G is a bipartite graph of order n , then γ - ( G ) ≥ 4 n + 1 - 1 - n . (2) For any negative integer k and any positive integer...

Signed total domination number of a graph

Bohdan Zelinka (2001)

Czechoslovak Mathematical Journal

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The signed total domination number of a graph is a certain variant of the domination number. If v is a vertex of a graph G , then N ( v ) is its oper neighbourhood, i.e. the set of all vertices adjacent to v in G . A mapping f : V ( G ) → { - 1 , 1 } , where V ( G ) is the vertex set of G , is called a signed total dominating function (STDF) on G , if ∑ x ∈ N ( v ) f ( x ) ≥ 1 for each v ∈ V ( G ) . The minimum of values ∑ x ∈ V ( G ) f ( x ) , taken over all STDF’s of G , is called the signed total domination number of G and denoted by γ s t ( G ) . A theorem stating lower bounds for γ s t ( G ) is...