Vertex irregular reflexive labeling of disjoint union of gear and book graphs

Title: Vertex irregular reflexive labeling of disjoint union of gear and book graphs
Creator: Alfarisi, Ridho; Ryan, Joe; Siddiqui, Muhammad Kamran; Dafik,; Agustin, Ika Hesti
Relation: Asian-European Journal of Mathematics Vol. 14, Issue 5, no. 2150078
Publisher Link: http://dx.doi.org/10.1142/S1793557121500789
Publisher: World Scientific
Resource Type: journal article
Date: 2021
Description: We define f: E(G) →{1, 2,...,ke} and f:V (G) →{0, 2,..., 2kv} for ke,kv N ∪{0}, where k =max{ke, 2kv}. The labeling f is called a vertex irregular reflexive k-labeling if any vertices have distinct weight which wf(u)≠wf(v) for any vertices in a graph G. The weight of a vertex u V (G) is defined as the sum of the labels of vertex and the labels of all edges incident this vertex. The smallest k for which such labeling exists is called reflexive vertex strength of G, denoted by rvs(G). In this paper, we determine the reflexive vertex strength of gear graphs, book graphs, triangular book graph and the disjoint union of gear graphs.
Subject: vertex irregular reflexive labeling; reflexive vertex strength; gear graphs; book graphs; triangular book graph
Identifier: http://hdl.handle.net/1959.13/1475433
Identifier: uon:49558
Identifier: ISSN:1793-5571
Language: eng
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