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On $(k,d)$-Hooked Skolem Graceful Graphs [PDF]

Journal of Combinatorics, Information and System Sciences 41 (2016) No. 1-2, 7-15, 2017
A graph $(p, q)$ graph $G = (V, E)$ is said to be $(k, d)$-hooked Skolem graceful if there exists a bijection $f:V (G)\rightarrow \{1, 2, \dots, p-1, p+1\}$ such that the induced edge labeling $g_f : E \rightarrow \{k, k+d, \dots, k+(n-1)d \}$ defined by $g_f (uv) = |f(u) - f(v)|$ $\forall uv \in E$ is also bijective, where $k$ and $d$ are positive ...
arxiv

Further results on super graceful labeling of graphs

AKCE International Journal of Graphs and Combinatorics, 2016
AbstractLet G=(V(G),E(G)) be a simple, finite and undirected graph of order p and size q. A bijection f:V(G)∪E(G)→{k,k+1,k+2,…,k+p+q−1} such that f(uv)=|f(u)−f(v)| for every edge uv∈E(G) is said to be a k-super graceful labeling of G. We say G is k-super graceful if it admits a k-super graceful labeling.
Gee-Choon Lau, Ho Kuen Ng, Wai Chee Shiu
openaire +3 more sources

Natural language processing analysis of the psychosocial stressors of mental health disorders during the pandemic. [PDF]

Npj Ment Health Res, 2023
Raveau MP +7 more
europepmc +1 more source

New graceful diameter-6 trees by transfers [PDF]

arXiv, 2014
Given a graph $G$, a labeling of $G$ is an injective function $f:V(G)\rightarrow\mathbb{Z}_{\ge 0}$. Under the labeling $f$, the label of a vertex $v$ is $f(v)$, and the induced label of an edge $uv$ is $|f(u) - f(v)|$. The labeling $f$ is graceful if the labels of the vertices are $\{0, 1, \ldots , |V(G)| - 1\}$, and the induced labels of the edges ...
arxiv

Joint reconstruction of neuron and ultrastructure via connectivity consensus in electron microscope volumes. [PDF]