کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
419292 | 683773 | 2015 | 10 صفحه PDF | دانلود رایگان |

Let G=(V(G),E(G))G=(V(G),E(G)) be a graph with vertex set V(G)V(G) and edge set E(G)E(G). The RR-graph of a graph GG, denoted by R(G)R(G), is the graph obtained from GG by adding a vertex veve and then joining veve to the end vertices of ee for each e∈E(G)e∈E(G). Let G1G1 and G2G2 be two vertex disjoint graphs. The RR-vertex join of G1G1 and G2G2, denoted by G1〈v〉G2, is the graph obtained from R(G1)R(G1) and G2G2 by joining every vertex of V(G1)V(G1) with every vertex of V(G2)V(G2). The RR-edge join of G1G1 and G2G2, denoted by G1〈e〉G2, is the graph obtained from R(G1)R(G1) and G2G2 by joining every vertex of I(G1)I(G1) with every vertex of V(G2)V(G2), where I(G1)I(G1) is the set of the added vertices of R(G1)R(G1). In this paper, we formulate the resistance distances and the Kirchhoff index of G1〈v〉G2 and G1〈e〉G2 respectively.
Journal: Discrete Applied Mathematics - Volume 187, 31 May 2015, Pages 130–139