Results 21 to 30 of about 72 (71)
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 8, Page 495-499, 2002., 2002 We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. As a consequence, we determine which graceful numbers are perfect.
Kiran R. Bhutani, Alexander B. Levin
wiley +1 more source
Power domination in Mycielskian of spiders
AKCE International Journal of Graphs and Combinatorics, 2022 The power domination problem in graphs consists of finding a minimum set of vertices [Formula: see text] that monitors the entire graph G governed by two ‘monitoring rules’- domination and propagation. A set [Formula: see text] is a power dominating set (
Seema Varghese +2 more
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Open Mathematics, 2017 An edge-magic total labeling of an (n,m)-graph G = (V,E) is a one to one map λ from V(G) ∪ E(G) onto the integers {1,2,…,n + m} with the property that there exists an integer constant c such that λ(x) + λ(y) + λ(xy) = c for any xy ∈ E(G).
Javed Sana +5 more
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Two extensions of Leech labeling to the class of all graphs
AKCE International Journal of Graphs and Combinatorics, 2022 Let [Formula: see text] be a tree of order n and let [Formula: see text] be an injective edge labeling of T. The weight of a path P is the sum of the labels of the edges of P and is denoted by [Formula: see text] If the set of weights of the [Formula ...
Seena Varghese +2 more
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Proof of a local antimagic conjecture [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 An antimagic labelling of a graph $G$ is a bijection $f:E(G)\to\{1,\ldots,E(G)\}$ such that the sums $S_v=\sum_{e\ni v}f(e)$ distinguish all vertices. A well-known conjecture of Hartsfield and Ringel (1994) is that every connected graph other than $K_2 ...
John Haslegrave
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AKCE International Journal of Graphs and Combinatorics, 2023 We introduce a concept in graph coloring motivated by the popular Sudoku puzzle. Let [Formula: see text] be a graph of order n with chromatic number [Formula: see text] and let [Formula: see text] Let [Formula: see text] be a k-coloring of the induced ...
J. Maria Jeyaseeli +3 more
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Computing the Radio Number via Multilevel Distance Labelings for Connected Graphs
Journal of Mathematics, Volume 2026, Issue 1, 2026.Suppose G is a connected graph. For any two vertices s and t, let dG (s,t) denote the distance between s and t in G. The diameter of G is the maximum distance between any pair of vertices, and it is denoted by diam(G). A multilevel distance labeling is a function VG⟶Z+, such that for any two vertices s ≠ t, we have d(s, t) + |f(s) − f(t)| ≥ diam(G) + 1.
Munawwar Hussain +5 more
wiley +1 more source
Sharp bounds for partition dimension of generalized Möbius ladders
Open Mathematics, 2018 The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing.
Hussain Zafar +4 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.Let H be a graph with h vertices and e edges. An edge‐magic‐total labeling of graph H is a bijective function g : V(H) ∪ E(H)⟶{1, 2, …, h + e} such that g(a) + g(a, b) + g(b) = k, ∀(a, b) ∈ E(H). When g : V(H)⟶{1, 2, …, h}, it is termed a super edge‐magic total labeling. We introduce the concept of a (c, d)‐cycle book graph, denoted by Book[(c, α), (d,
Baki Swita +8 more
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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.This article explores numerous significant additive topological indices based on degrees for linear functional graphs over finite‐dimensional vector spaces. Specifically, we derive some unique topological indices, such as the eccentricity‐based indices and the Wiener index.
Vinnarasi L. +4 more
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