let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...

On the one hand, Conceptual Graphs are widely used in natural language processing systems. On the other hand, information fusion community lacks of tools and methods for knowledge representation. Using natural language processing techniques for information fusion is a new field of interest in the fusion community. Our aim is to take the advantage of both communities and propose a framework for ...

let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

The complete double vertex graph $M_2(G)$ of $G$ is defined as the whose vertices are $2$-multisubsets $V(G)$, and two such adjacent in if their symmetric difference (as multisets) a pair $G$. In this paper we exhibit an infinite family graphs (containing Hamiltonian non-Hamiltonian graphs) for which Hamiltonian.

The cyclicity of a hypergraph is an e ciently computable integer that extends the notion of the cyclomatic number of a graph The formula for the cyclicity is suggested by the join invariant of an acyclic hypergraph which is the multiset of all joining sets in any of its join trees Once we gure out how the multiplicity of a joining set depends on the structure of the acyclic hypergraph we de ne ...

Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices...