A 2-join is an edge cutset that naturally appears in decomposition of several classes of graphs closed under taking induced subgraphs, such as perfect graphs and claw-free graphs. In this paper we construct combinatorial polynomial time algorithms for finding a maximum weighted clique, a maximum weighted stable set and an optimal coloring for a class of perfect graphs decomposable by 2-joins: t...

The atom graph of a graph is the graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all possible atom trees of this graph. We provide two efficient algorithms for computing this atom graph, with a complexity in O(min(n log n, nm,n(n+m)) time, which is no more than the complexity of computing the atoms in the gene...

In this paper the concept of inverse domintion in some operations on bipolar fuzzy graphs was introduced and investigated bound γ8 are obtained like union, join,Cartesian product, strong product composition.

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

The graph G of order n is an L-borderenergetic which means it has the same Laplacian energy as complete Kn. In this paper, we find that combination bipartite graphs and stars can construct infinite numbers classes graphs. We give two Lborderenergetic under operators union, join their mixed. This research could provide experience for further study structural characteristics

We give new observations on the mixing dynamics of a continuous-time quantum walk on circulants and their bunkbed extensions. These bunkbeds are defined through two standard graph operators: the join G + H and the Cartesian product G ⊕ H of graphs G and H . Our results include the following: • The quantum walk is average uniform mixing on circulants with bounded eigenvalue multiplicity. This ex...

The “standard” method of implementing composition is to perform join and projection as one combined operation and then to remove the duplicates from the result of this operation as a separate step. When a hash-based or sort-merge algorithm is used for the join operation and the size of the result is large, duplicates cannot be eliminated at the same time the join is being performed. In this pap...