JOINS, CORONAS AND THEIR VERTEX-EDGE WIENER POLYNOMIALS

被引:1
作者
Azari, Mahdieh [1 ]
Iranmanesh, Ali [2 ]
机构
[1] Islamic Azad Univ, Kazerun Branch, Dept Math, POB 73135-168, Kazerun, Iran
[2] Tarbiat Modares Univ, Fac Math Sci, Dept Pure Math, POB 14115-137, Tehran, Iran
来源
TAMKANG JOURNAL OF MATHEMATICS | 2016年 / 47卷 / 02期
关键词
Distance; topological index; graph polynomial; graph operation;
D O I
10.5556/j.tkjm.47.2016.1824
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. The vertex-edge Wiener polynomial of G is a generating function whose first derivative is a q-analog of the vertex-edge Wiener index. Two possible distances D-1(u, e|G) and D-2(u, e|G) between a vertex u and an edge e of G can be considered and corresponding to them, the first and second vertex-edge Wiener indices of G, and the first and second vertex-edge Wiener polynomials of G are introduced. In this paper, we study the behavior of these indices and polynomials under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs.
引用
收藏
页码:163 / 178
页数:16
相关论文
共 29 条
[1]   THE SECOND EDGE-WIENER INDEX OF SOME COMPOSITE GRAPHS [J].
Azari, M. ;
Iranmanesh, A. .
MISKOLC MATHEMATICAL NOTES, 2014, 15 (02) :305-316
[2]  
Azari M., 2014, TOPICS CHEM GRAPH TH, P69
[3]  
Azari M, 2013, MATCH-COMMUN MATH CO, V69, P69
[4]  
Azari M, 2012, UTILITAS MATHEMATICA, V87, P151
[5]  
Azari M, 2011, ARS COMBINATORIA, V100, P113
[6]   The edge-Wiener index of a graph [J].
Dankelmann, P. ;
Gutman, I. ;
Mukwembi, S. ;
Swart, H. C. .
DISCRETE MATHEMATICS, 2009, 309 (10) :3452-3457
[7]  
Darafsheh MR, 2011, ARS COMBINATORIA, V100, P289
[8]  
Diudea MV, 1995, MATCH-COMMUN MATH CO, P71
[9]  
Diudea MV, 2002, MATCH-COMMUN MATH CO, P109
[10]   Vertex-Weighted Wiener Polynomials for Composite Graphs [J].
Doslic, Tomislav .
ARS MATHEMATICA CONTEMPORANEA, 2008, 1 (01) :66-80