W 树 W T ( n , k ) 的奇数优美标签及其二分联盟

Q4 Mathematics

Utilitas Mathematica Pub Date : 2024-01-08 DOI:10.61091/um118-05

Abaid ur Rehman Virk, A. Riasat

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引用次数: 0

摘要

假设 G=(V(G),E(G)) 是一个有 p 个顶点和 q 条边的图。如果存在注入λ:V(G)→0,1,2,......,2q-1，给每条边 xy 赋上标签或权重|λ(x)-λ(y)|，结果边标签集为 1,3,5,......,2q-1，那么大小为 q 的图 G 称为奇数优美图。这一概念由 Gananajothi 于 1991 年提出。在本文中，我们将研究 W 树的奇数优美标签，记为 WT(n,k)。

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Odd Graceful Labeling of W -Tree W T ( n , k ) and its Disjoint Union

Let G=(V(G),E(G)) be a graph with p vertices and q edges. A graph G of size q is said to be odd graceful if there exists an injection λ:V(G)→0,1,2,…,2q−1 such that assigning each edge xy the label or weight |λ(x)–λ(y)| results in the set of edge labels being 1,3,5,…,2q−1. This concept was introduced in 1991 by Gananajothi. In this paper, we examine the odd graceful labeling of the W-tree, denoted as WT(n,k).

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来源期刊

Utilitas Mathematica 数学-统计学与概率论

CiteScore

0.50

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Utilitas Mathematica publishes papers in all areas of statistical designs and combinatorial mathematics, including graph theory, design theory, extremal combinatorics, enumeration, algebraic combinatorics, combinatorial optimization, Ramsey theory, automorphism groups, coding theory, finite geometries, chemical graph theory, etc., as well as the closely related area of number-theoretic polynomials for enumeration.