Please use this identifier to cite or link to this item: https://ir.swu.ac.th/jspui/handle/123456789/13528
ชื่อเรื่อง: Proper-path colorings in graph operations
ผู้แต่ง: Andrews E.
Laforge E.
Lumduanhom C.
Zhang P.
Keywords: Coloring
Graphic methods
Connected graph
Connection number
Cut vertex
Edge coloring
Graph operations
Iterated line graphs
Lower and upper bounds
Path colorings
Graph theory
วันที่เผยแพร่: 2016
บทคัดย่อ: Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of P are colored the same. An edge coloring is a proper-path coloring of G if every pair u, v of distinct vertices of G are connected by a proper u - v path in G. The minimum number of colors required for a properpath coloring of G is the proper connection number pc(G) of G. We study proper-path colorings in those graphs obtained by some well-known graph operations, namely line graphs, powers of graphs, coronas of graphs and vertex or edge deletions. Proper connection numbers are determined for all iterated line graphs and powers of a given connected graph. For a connected graph G, sharp lower and upper bounds are established for the proper connection number of (i) the k-iterated corona of G in terms of pc(G) and k and (ii) the vertex or edge deletion graphs G - v and G - e where visa non-cut-vertex of G and e is a non-bridge of G in terms of pc(G) and the degree of v. Other results and open questions are also presented. © 2016 Charles Babbage Research Centre. All rights reserved.
URI: https://ir.swu.ac.th/jspui/handle/123456789/13528
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85045018656&partnerID=40&md5=c1c866f47ad8918a76316bf046e6c5e6
ISSN: 8353026
Appears in Collections:Scopus 1983-2021

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