Displaying similar documents to “On γ -labelings of oriented graphs”

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...

On k -pairable graphs from trees

Zhongyuan Che (2007)

Czechoslovak Mathematical Journal

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The concept of the k -pairable graphs was introduced by Zhibo Chen (On k -pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p ( G ) , called the pair length of a graph G , as the maximum k such that G is k -pairable and p ( G ) = 0 if G is not k -pairable for any positive integer k . In this paper, we answer the two open questions raised by Chen in the case that the graphs...

Distance in stratified graphs

Gary Chartrand, Lisa Hansen, Reza Rashidi, Naveed Sherwani (2000)

Czechoslovak Mathematical Journal

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A graph G is stratified if its vertex set is partitioned into classes, called strata. If there are k strata, then G is k -stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color X in a stratified graph G , the X -eccentricity e X ( v ) of a vertex v of G is the distance between v and an X -colored vertex furthest from v . The minimum X -eccentricity among the vertices of G is the X -radius r a d X G of G ...

Containers and wide diameters of P 3 ( G )

Daniela Ferrero, Manju K. Menon, A. Vijayakumar (2012)

Mathematica Bohemica

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The P 3 intersection graph of a graph G has for vertices all the induced paths of order 3 in G . Two vertices in P 3 ( G ) are adjacent if the corresponding paths in G are not disjoint. A w -container between two different vertices u and v in a graph G is a set of w internally vertex disjoint paths between u and v . The length of a container is the length of the longest path in it. The w -wide diameter of G is the minimum number l such that there is a w -container of length at most l between any pair...