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All Journal Journal of the Indonesian Mathematical Society Jurnal Matematika Integratif
Sri Nurhayati
Universitas Gadjah Mada
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Transportation

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An Edge Irregular Reflexive k−labeling of Comb Graphs with Additional 2 Pendants Sri Nurhayati; Yeni Susanti
Jurnal Matematika Integratif Vol 19, No 1: April 2023
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (467.384 KB) | DOI: 10.24198/jmi.v19.n1.41624.89-108

Abstract

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.
THE NON-BRAID GRAPH OF DIHEDRAL GROUP Dn Hubbi Muhammad; Rambu Maya Imung Maharani; Sri Nurhayati; Mira Wadu; Yeni Susanti
Journal of the Indonesian Mathematical Society VOLUME 30 NUMBER 1 (MARCH 2024)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.1.1401.110-120

Abstract

We introduce the non-braid graph of a group G, denoted by ζ(G), as a graph with vertex set G \ B(G), where B(G) is the braider of G, defined as the set {x ∈ G | (∀y ∈ G)xyx = yxy}, and two distinct vertices x and y are joined by an edge if and only if xyx ̸ = yxy. In this paper particularly we give the independent number, the vertex chromatic number, the clique number, and the minimum vertex cover of non-braid graph of dihedral group Dn
Co-Authors Hubbi Muhammad Mira Wadu Rambu Maya Imung Maharani Yeni Susanti Yeni Susanti