a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}, called the signature of S. The ×-line sigraph of S denoted by L×(S) is a sigraph defined on the line graph L(S u) of the graph Su by assigning to each edge ef of L(Su), the product of si...

Security of a network is important to all organizations, personal computer users, and the military. With the invention of the Internet, major concern is about the security and the history of security allows a better understanding of the emergence of security technology. One of the ways to secure businesses from the Internet is through firewalls and encryption mechanisms. A network can be design...

A signedgraph (or sigraph in short) S is a graph G in which each edge x carries a value [Formula: see text] called its sign   denoted specially as [Formula: see text]. Given a sigraph S,  H = L(S)   called the line sigraph of S is that sigraph in which edges of S are represented as vertices, two of these vertices are defined to be adjacent whenever the corresponding edges in S have a vertex in ...

A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V,E) and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a positive integer n > 1, the unitary Cayley graph Xn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes set of all units of the ring Zn, then two vertices a, b are adjacent if and only if a...

abstract many studies have been conducted on the characteristics of hydraulic jump over gradually expanding cross sections, but comparatively few have been carried out on basins with convergent wall. in the present research, the hydraulic jump characteristic of the stilling basin with convergent wall has been investigated. the main objective of this research is evaluation of conjugate depths ra...

hydraulic jump on adverse stilling basin is an unstable phenomenon which causes some complexities in controlling of the   jump. this paper considers the stability of free hydraulic jump on adverse stilling basins from a theoretical point of view. a minimum value of upstream froude number is needed to produce the free hydraulic jump on adverse stilling basins which was presented by a theoretical...