Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1403
1
1
gregorian
2024
4
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19
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online
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fulltext
en
On Local Antimagic Chromatic Number of Graphs with Cut-vertices
عمومى
General
پژوهشي
Research paper
<div style="text-align: justify;">An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it is a bijection f:E →{1,... ,|E|} such that for any pair of adjacent vertices x and y, f<sup>+</sup>(x)≠ f<sup>+</sup>(y), where the induced vertex label f<sup>+</sup>(x)= ∑ f(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by X<sub>la</sub>(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, the sharp lower bound of the local antimagic chromatic number of a graph with cut-vertices given by pendants is obtained. The exact value of the local antimagic chromatic number of many families of graphs with cut-vertices (possibly given by pendant edges) are also determined. Consequently, we partially answered Problem 3.1 in [Local antimagic vertex coloring of a graph, Graphs and Combin., 33, (2017), 275--285].</div>
Local antimagic labeling, Local antimagic chromatic number, Cut-vertices, Pendants.
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http://ijmsi.ir/browse.php?a_code=A-10-2087-4&slc_lang=en&sid=1
Gee-Choon
Lau
geeclau@yahoo.com
`100319475328460010616`

100319475328460010616
Yes
Faculty of Computer & Mathematical Sciences, Universiti Teknologi MARA (UiTM) Malaysia
Wai-Chee
Shiu
wcshiu@associate.hkbu.edu.hk
`100319475328460010617`

100319475328460010617
No
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Ho-Kuen
Ng
ho-kuen.ng@sjsu.edu
`100319475328460010618`

100319475328460010618
No
Department of Mathematics, San José State University, San José CA 95192 USA