Browsing by Author "Nadeem, M.F."

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Edge Irregularity Strength of Certain Families of Comb Graph
(Universidad Catolica del Norte, 2020) Zhang, X.; Cancan, M.; Nadeem, M.F.; Imran, M.
Edge irregular mapping or vertex mapping h: V (U)-→ l, 2, 3, 4,..., s is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wth(cd) = h(c)+h(d), \∀c, d∈ V (U) and \∀cd ∈ E(U). Edge irregularity strength denoted by es(U) is a minimum positive integer use to label vertices to form edge irregular labeling. In this paper, we find exact value of edge irregularity strength of different families of comb graph. © 2020 Xiujun Zhang, Murat Cancan, Muhammad Faisal Nadeem, and Muhammad Imran.
Further Results on Edge Irregularity Strength of Some Graphs
(Universidad Catolica del Norte, 2024) Imran, M.; Cancan, M.; Nadeem, M.F.; Ali, Y.
The focal point of this paper is to ascertain the precise value of edge irregularity strength of various finite, simple, undirected and captivating graphs, including the splitting graph, shadow graph, jewel graph, jellyfish graph and m copies of 4-pan graph. © (2024), (Universidad Catolica del Norte). All rights reserved.
On Edge Irregularity Strength of Certain Families of Snake Graph
(Abdus Salam School of mathematical Sciences, 2023) Nadeem, M.F.; Cancan, M.; Imran, M.; Ali, Y.
Edge irregular mapping or vertex mapping β: V (U)→ {1, 2, 3,…, s} is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wtβ(cd) =β(c)+β(d), ∀c, d ∈ V (U) and cd ∈ E(U). Edge irregularity strength denoted by es(U) is a minimum positive integer used to label vertices to form edge irregular labeling. The aim of this paper is to determine the exact value of edge irregularity strength of different families of snake graph. © (2023). All Rights Reserved.
Partition Dimension of Generalized Peterson and Harary Graphs
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Nadeem, M.F.; Azeem, M.; Farahani, M.R.; Cancan, M.
The distance of a connected, simple graph (Formula presented) is denoted by d(α1, α2), which is the length of a shortest path between the vertices α1,α2 (Formula presented) V((Formula presented)), where V((Formula presented)) is the vertex set of (Formula presented). The l-ordered partition of V((Formula presented)) is K = {K1, K2,..., Kl}. A vertex α (Formula presented) V((Formula presented)), and r(α|K) = {d(α, K1), d(α, K2),..., d(α, Kl)} be a l-tuple distances, where r(α|K) is the representation of a vertex a with respect to set K. If r(a|K) of a is unique, for every pair of vertices, then K is the resolving partition set of V((Formula presented)). The minimum number l in the resolving partition set K is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, Pλx and proved that these families have bounded partition dimension. © 2021. All Rights Reserved.
Results on Super Edge Magic Deficiency of Some Well-Known Classes of Finite Graphs
(Universidad Catolica del Norte, 2024) Imran, M.; Cancan, M.; Nadeem, M.; Nadeem, M.F.
A graph Ω(Λ, Γ) is considered super edge magic if there exists a bijective function φ: Λ(Ω)∪Γ(Ω) −→ {1, 2, 3,…, |Λ(Ω)|+|Γ(Ω)|} such that φ(τ1)+φ(τ1τ2)+φ(τ2) is a constant for every edge τ1τ2 ∈ Γ(Ω), and φ(Λ(Ω)) = {1, 2, 3,…, |Λ(Ω)|}. Furthermore, the super edge magic deficiency of a graph Ω, denoted as μs(Ω), is either the minimum non-negative integer η such that Ω ∪ ηK1 is a super edge magic graph or +∞ if such an integer η does not exist. In this paper, we investigate the super edge magic deficiency of certain families of graphs. © (2024), (SciELO-Scientific Electronic Library Online). All Rights Reserved.