Rainbow connection number of amalgamation of some graphs

Let be a nontrivial connected graph. For , we define a coloring of the edges of such that adjacent edges can be colored the same. A path in is a rainbow path if no two edges of are colored the same. A rainbow path connecting two vertices and in is called rainbow - path. A graph is said rainbow-conne...

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Bibliographic Details
Published inAKCE International Journal of Graphs and Combinatorics Vol. 13; no. 1; pp. 90 - 99
Main Authors Fitriani, D., Salman, A.N.M.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.04.2016
Taylor & Francis Group
Subjects
Amalgamation
Complete graph
Fan
Rainbow connection number
Wheel
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Summary:Let be a nontrivial connected graph. For , we define a coloring of the edges of such that adjacent edges can be colored the same. A path in is a rainbow path if no two edges of are colored the same. A rainbow path connecting two vertices and in is called rainbow - path. A graph is said rainbow-connected if for every two vertices and of , there exists a rainbow - path. In this case, the coloring is called a rainbow -coloring of . The minimum such that has a rainbow -coloring is called the rainbow connection number of . For and , let be a finite collection of graphs and each has a fixed vertex called a terminal. The amalgamation is a graph formed by taking all the 's and identifying their terminals. We give lower and upper bounds for the rainbow connection number of for any connected graph . Additionally, we determine the rainbow connection number of amalgamation of either complete graphs, or wheels, or fans.
ISSN:0972-8600
2543-3474
DOI:10.1016/j.akcej.2016.03.004