TY  - JOUR
ID  - Awanis2022
LB  - Awanis2022
AU  - Awanis, Zata Yumni
AU  - Salman, A.N.M.
TI  - The strong 3-rainbow index of some certain graphs and its amalgamation
ST  - The strong 3-rainbow index of some certain graphs and its amalgamation
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 4
SP  - 527
EP  - 547
DO  - https://doi.org/10.7494/OpMath.2022.42.4.527
UR  - https://doi.org/10.7494/OpMath.2022.42.4.527
AB  - We introduce a strong \(k\)-rainbow index of graphs as modification of well-known \(k\)-rainbow index of graphs. A tree in an edge-colored connected graph \(G\), where adjacent edge may be colored the same, is a rainbow tree if all of its edges have distinct colors. Let \(k\) be an integer with \(2\leq k\leq n\). The strong \(k\)-rainbow index of \(G\), denoted by \(srx_k(G)\), is the minimum number of colors needed in an edge-coloring of \(G\) so that every \(k\) vertices of \(G\) is connected by a rainbow tree with minimum size. We focus on \(k=3\). We determine the strong \(3\)-rainbow index of some certain graphs. We also provide a sharp upper bound for the strong \(3\)-rainbow index of amalgamation of graphs. Additionally, we determine the exact values of the strong \(3\)-rainbow index of amalgamation of some graphs.
KW  - amalgamation
KW  - rainbow coloring
KW  - rainbow Steiner tree
KW  - strong \(k\)-rainbow index
SN  - 1232-9274
ER  -