All trees of diameter five are graceful
نویسندگان
چکیده
منابع مشابه
Odd-graceful Labelings of Trees of Diameter 5
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}. We show here that any forest whose components are caterpillars is odd...
متن کاملSome New Classes of Graceful Diameter Six Trees
Here we denote a diameter six tree by (a0; a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr), where a0 is the center of the tree; ai, i = 1, 2, . . . ,m, bj , j = 1, 2, . . . , n, and ck, k = 1, 2, . . . , r are the vertices of the tree adjacent to a0; each ai is the center of a diameter four tree, each bj is the center of a star, and each ck is a pendant vertex. Here we give graceful...
متن کاملSome new graceful generalized classes of diameter six trees
Here we denote a diameter six tree by (c; a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr), where c is the center of the tree; ai, i = 1, 2, . . . ,m, bj, j = 1, 2, . . . , n, and ck, k = 1, 2, . . . , r are the vertices of the tree adjacent to c; each ai is the center of a diameter four tree, each bj is the center of a star, and each ck is a pendant vertex. Here we give graceful lab...
متن کاملInteger-Magic Spectra of Trees of Diameter Five
For any h ∈ Z, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh−{0} such that the induced vertex set labeling l : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. For a given graph G, the set of all h ∈ Z+ for which G is h-magic is called the integermagic spectrum of G and is denoted by IM (G). In this paper, we will determine the integer-magic sp...
متن کاملModular Edge-Graceful Trees
Ryan Jones, Western Michigan University We introduce a modular edge-graceful labeling of a graph a dual concept to the common graceful labeling. A 1991 conjecture known as the Modular Edge-Graceful Tree Conjecture states that every tree of order n where n 6≡ 2 (mod 4) is modular edge-graceful. We show that this conjecture is true. More general results and questions on this topic are presented.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00233-8