Special Graceful Labelings of Irregular Fences and Lobsters
نویسندگان
چکیده
منابع مشابه
On d-graceful labelings
We introduce a generalization of the well known concept of a graceful labeling. Given a graph Γ with e = d · m edges, we call d-graceful labeling of Γ an injective function from(m + 1)}. In the case of d = 1 and of d = e we find the classical notion of a graceful labeling and of an odd graceful labeling, respectively. Also, we call d-graceful α-labeling of a bipartite graph Γ a d-graceful label...
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A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
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7 Partial cubes are graphs that allow isometric embeddings into hypercubes. -graceful labelings of partial cubes are introduced as a natural extension of graceful labelings of trees. It is shown that several classes of partial cubes are -graceful, for instance even 9 cycles, Fibonacci cubes, and (newly introduced) lexicographic subcubes. The Cartesian product of -graceful partial cubes is again...
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متن کاملOn certain classes of graceful lobsters
A (simple undirected) graph G = (V,E) with m edges is graceful if it has a distinct vertex labeling f : V −→ {0, 1, 2, 3, . . . ,m} which induces a set of distinct edge labels {|f(u)− f(v)| | uv ∈ E, u, v ∈ V }. The famous Ringel-Kotzig conjecture [9, 15] is that all trees are graceful. The base of a tree T is obtained from T by deleting its one-degree vertices. A caterpillar is a tree whose ba...
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ژورنال
عنوان ژورنال: Universal Journal of Mathematics and Applications
سال: 2019
ISSN: 2619-9653
DOI: 10.32323/ujma.520682