# More on p* Graceful Graphs

## Related Articles

- SHARP UPPER AND LOWER BOUNDS ON THE NUMBER OF SPANNING TREES IN CARTESIAN PRODUCT OF GRAPHS. AZARIJA, JERNEJ // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 4, p785
Let G1 and G2 be simple graphs and let n1 = | V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees t in the Cartesian product G1â–¡G2 of G1 and G2. We show that: Ï„G1â–¡G2 â‰¥...

- On graphs whose chromatic transversal number is two. Ayyaswamy, S. K.; Natarajan, C. // Proyecciones - Journal of Mathematics;2011, Vol. 30 Issue 1, p59
In this paper we characterize the class of trees, block graphs, cactus graphs and cubic graphs for which the chromatic transversal domination number is equal to two.

- WEAK SATURATION NUMBERS FOR SPARSE GRAPHS. FAUDREE, RALPH J.; GOULD, RONALD J.; JACOBSON, MICHAEL S. // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 4, p677
For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e âˆ‰ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat (n, F). A graph G is weakly F-saturated if there is an ordering of the...

- Absolutely Harmonious Labeling of Graphs. Seenivasan, M.; Lourdusamy, A. // International Journal of Mathematical Combinatorics;Jun2011, Vol. 2, p40
Absolutely harmonious labeling f is an injection from the vertex set of a graph G with q edges to the set {0, 1, 2, ï¿½, q - 1}, if each edge uv is assigned f(u) + f(v) then the resulting edge labels can be arranged as a0, a1, a2, ï¿½, aq-1 where ai = q - i or q + i, 0 = i = q - 1 ....

- SUPERMAGIC GRAPHS HAVING A SATURATED VERTEX. IVANČO, JAROSLAV; POLLÁKOVÁ, TATIANA // Discussiones Mathematicae: Graph Theory;2014, Vol. 34 Issue 1, p75
A graph is called supermagic if it admits a labeling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we establish some conditions for graphs with a saturated vertex...

- A CONSTRUCTION OF AÎ²-COALESCENT VIA THE PRUNING OF BINARY TREES. ABRAHAM, ROMAIN; DELMAS, JEAN-FRANÇOIS // Journal of Applied Probability;Sep2013, Vol. 50 Issue 3, p772
Considering a random binary tree with n labelled leaves, we use a pruning procedure on this tree in order to construct a Î²(3/2, Â½)-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous's continuum random tree, to construct a...

- On Family of Graphs with Minimum Number of Spanning Trees. Bogdanowicz, Zbigniew // Graphs & Combinatorics;Nov2013, Vol. 29 Issue 6, p1647
We show that there is a well-defined family of connected simple graphs Î›( n, m) on n vertices and m edges such that all graphs in Î›( n, m) have the same number of spanning trees, and if $${G \in \Lambda(n, m)}$$ then the number of spanning trees in G is strictly less than the number of...

- STRONG EQUALITY BETWEEN THE ROMAN DOMINATION AND INDEPENDENT ROMAN DOMINATION NUMBERS IN TREES. CHELLALI, MUSTAPHA; RAD, NADER JAFARI // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 2, p337
A Roman dominating function (RDF) on a graph G = (V, E) is a function f : V â†’ {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF is the value f(V (G)) = Î£u âˆˆ V(G) f(u). An RDF f in...

- THE CROSSING NUMBERS OF PRODUCTS OF PATH WITH GRAPHS OF ORDER SIX. KLEŠČ, MARIÁN; PETRILLOVÁ, JANA // Discussiones Mathematicae: Graph Theory;2013, Vol. 33 Issue 3, p571
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products Gâ–¡Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers...