Note on group irregularity strength of disconnected graphs
We investigate the group irregularity strength (sg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group ๐ of order s, there exists a function f : E(G) โ ๐ such that the sums of edge labels at every vertex are distinct. So far it was not known if sg(G) is finite for disconne...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-03-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/math.2018.16.issue-1/math-2018-0017/math-2018-0017.xml?format=INT |
| Summary: | We investigate the group irregularity strength (sg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group ๐ of order s, there exists a function f : E(G) โ ๐ such that the sums of edge labels at every vertex are distinct. So far it was not known if sg(G) is finite for disconnected graphs. In the paper we present some upper bound for all graphs. Moreover we give the exact values and bounds on sg(G) for disconnected graphs without a star as a component. |
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| ISSN: | 2391-5455 |