a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

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in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

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 significant challenge in evaluating network security stems from the scale of modern enterprise networks and the vast number of vulnerabilities regularly found in software applications. A common technique to deal with this complexity is attack graphs, where a tool automatically computes all possible ways a system can be broken into by analyzing the configuration of each host, the network, and ...

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

introduction one of the most vulnerable water resources against contamination is ground water table. these resources are exposed to contamination in various forms. identifying and controlling contamination in these resources are more difficult and costly than surface waters. also because of the persistence of contamination in these resources, the best way to prevent their contamination is to id...

An attack graph is a data structure representing how an attacker can chain together multiple attacks to expand their influence within a network (often in an attempt to reach some set of goal states). Restricting attack graph size is vital for the execution of high degree polynomial analysis algorithms. However, we find that the most widely-cited and recently-used ‘condition/exploit’ attack grap...