The rainbow vertex connection number of edge corona product graphs

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Fauziah, D.A.^1^2 ; Dafik^1^3 ; Agustin, I.H.^1^2 ; Alfarisi, R.^1^3

CGANT, University of Jember, Indonesia^1

Mathematics Depart, University of Jember, Indonesia^2

Mathematics Edu. Depart, University of Jember, Indonesia^3

关键词: Adjacent vertices;    Connection number;    Cycle and path;    Graph G;    Product graph;    Product of graphs;    Vertex coloring;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012020/pdf
DOI  :  10.1088/1755-1315/243/1/012020

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Let G1, G2 be a special graphs with vertices of G1 1,2,, n and edges of G1 1,2, m. The generalized edge corona product of graphs G1 and G2, denoted by G 1G 1 is obtained by taking one copy of graph G1 and m copy of G2 , thus for each edge ek = ij of G, joining edge between the two end-vertices i, j of ek and each vertex of the k-copy of G2 . A rainbow vertex-coloring graph G where adjacent vertices u-v and its internal vertices have distinct colors. A path is called a rainbow path if no two verticess of the path have the same color. A rainbow vertex-connection number of graph G is minimun number of colors in graph G to connected every two distinct internal vertices u and v such that a graph G naturally rainbow vertex-connected, denoted by rvc (G). In this paper, we determine minimum integer for rainbow vertex coloring of edge corona product on cycle and path such as PnPm, PnCm, CnPm, and CnCm .