Results 41 to 50 of about 60,649 (158)
Efficient enumeration of graceful permutations [PDF]
arXiv, 2006 A graceful n-permutation is a graceful labeling of an n-vertex path P_n. In this paper we improve the asymptotic lower bound on the number of such permutations from (5/3)^n to 2.37^n. This is a computer-assisted proof based on an effective algorithm that enumerates graceful n-permutations. Our algorithm is also presented in detail.
arxiv
Graceful labelling of the union of paths and cycles
Discrete Mathematics, 1999 Frucht and Salinas (Ars. Combin. 20 (1985) 143–157) have proved that C4∪Pn is graceful, for every n⩾3, and they have conjectured that Cs∪Pn is graceful if n+s⩾7. In this paper we show that Cs∪Pn is graceful if s⩾5 and n⩾(s+5)/2.
Sheshayya A. Choudum +1 more
openaire +2 more sources
On alpha labeling of tensor product of paths and cycles. [PDF]
Heliyon, 2023 L U, G R.
europepmc +1 more source
Odd-graceful labelings of trees of diameter 5 [PDF]
arXiv, 2008 A difference vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy the weight |f(x)-f(y)|. A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V(G) to {0,1,...,2n-1} such that the induced weights are {1,3,...,2n-1}.
arxiv
A structural approach to the graceful coloring of a subclass of trees. [PDF]
Heliyon, 2023 D L, S DY.
europepmc +1 more source
On certain classes of graceful lobsters [PDF]
arXiv, 2013 A graph G=(V,E) with m edges is graceful if it has a distinct vertex labeling f, a map from V into the set{0,1,2,3,...,m} which induces a distinct edge labeling |f(u)-f(v)| for edges uv in E. The famous Ringel-Kotzig conjecture (1964) is that all trees are graceful. The base of a tree T is obtained from T by deleting its one-degree vertices.
arxiv
A new graceful labeling for pendant graphs [PDF]
Aequationes mathematicae, 2013 A graceful labeling of a graph G with q edges is an injective assignment of labels from {0, 1, . . . , q} to the vertices of G so that when each edge is assigned the absolute value of the difference of the vertex labels it connects, the resulting edge labels are distinct.
openaire +2 more sources
Graphic Groups, Graph Homomorphisms, and Graphic Group Lattices in Asymmetric Topology Cryptography. [PDF]
Entropy (Basel), 2023 Zhao M, Wang H, Yao B.
europepmc +1 more source
Ladder and Subdivision of Ladder Graphs with Pendant Edges are Odd Graceful [PDF]
arXiv, 2016 The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln + mk1 is odd graceful.
arxiv
Applying Skolem Sequences to Gracefully Label New Families of Triangular Windmills [PDF]
arXiv, 2020 A function $f$ is a \textit{graceful labelling} of a graph $G=(V,E)$ with $m$ edges if $f$ is an injection $f:V\mapsto \{0,1,2,\dots,m\}$ such that each edge $uv \in E$ is assigned the label $|f(u)-f(v)|$, and no two edge labels are the same. If a graph G has a graceful labelling, we say that $G$ itself is graceful.
arxiv