## Volume 4, Issue 4

### ارسال های اخیر

• #### A dynamic domination problem in trees ﻿

(University of Isfahan, 2015-12-01)
‎We consider a dynamic domination problem for graphs in which an infinite‎ ‎sequence of attacks occur at vertices with guards and the guard at the‎ ‎attacked vertex is required to vacate the vertex by moving to a neighboring‎ ...

• #### A classification of finite groups with integral bi-Cayley graphs ﻿

(University of Isfahan, 2015-12-01)
The bi-Cayley graph of a finite group \$G\$ with respect to a subset \$Ssubseteq G\$‎, ‎which is denoted by \$BCay(G,S)\$‎, ‎is the graph with‎ ‎vertex set \$Gtimes{1,2}\$ and edge set \${{(x,1)‎, ‎(sx,2)}mid xin G‎, ‎ sin S}\$‎. ...

• #### Broadcast domination in Tori ﻿

(University of Isfahan, 2015-12-01)
A broadcast on a graph \$G\$ is a function \$f‎ : ‎V(G) rightarrow {0‎, ‎1,dots‎, ‎diam(G)}\$ such that for every vertex \$v in V(G)\$‎, ‎\$f(v) leq e(v)\$‎, ‎where \$diam(G)\$ is the diameter of \$G\$‎, ‎and \$e(v)\$ is the ...

• #### On the harmonic index of graph operations ﻿

(University of Isfahan, 2015-12-01)
‎‎The harmonic index of a connected graph \$G\$‎, ‎denoted by \$H(G)\$‎, ‎is‎ ‎defined as \$H(G)=sum_{uvin E(G)}frac{2}{d_u+d_v}\$‎ ‎where \$d_v\$ is the degree of a vertex \$v\$ in G‎. ‎In this paper‎, ‎expressions for the Harary ...

• #### The resistance distance and the Kirchhoff index of the \$k\$-th semi total point graphs ﻿

(University of Isfahan, 2015-12-01)
‎The \$k\$-th semi-total point graph \$R^k(G)\$ of a graph \$G\$‎, ‎is a graph obtained from \$G\$ by adding \$k\$ vertices corresponding to each edge and connecting them to the endpoints of the edge considered‎. ‎In this paper‎, ...

• #### Chromatic and clique numbers of a class of perfect graphs ﻿

(University of Isfahan, 2015-12-01)
‎Let \$p\$ be a prime number and \$n\$ be a positive integer‎. ‎The graph‎ ‎\$G_p(n)\$ is a graph with vertex set \$[n]={1‎, ‎2,ldots‎, ‎n}\$‎, ‎in‎ ‎which there is an arc from \$u\$ to \$v\$ if and only if \$uneq v\$ and‎ ‎\$pnmid u+v\$‎. ...