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 ...

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

The F-index of a graph G is the sum of the cubes of the degrees of the vertices of G. In this paper, explicit expressions for the F-index of different transformation graphs of type Gxyz with x, y, z ∈ {−,+} are obtained. F-index for semitotal point graph and semitotal line graph are also obtained here. MSC (2010): Primary: 05C35; Secondary: 05C07, 05C40

A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.