A graph with forbidden transitions is a pair (G,FG) where G := (VG, EG) is a graph and FG is a subset of the set {({y, x}, {x, z}) ∈ E G}. A path in a graph with forbidden transitions (G,FG) is a path in G such that each pair ({y, x}, {x, z}) of consecutive edges does not belong to FG. It is shown in [S. Szeider, Finding paths in graphs avoiding forbidden transitions, DAM 126] that the problem ...

Rainbow vertex-connection number is the minimum colors assignment to vertices of graph, such that each vertex connected by a path whose edges have distinct and denoted . The rainbow connection can be applied graphs resulting from operations. One methods create new graph perform operations between two graphs. Thus, this research uses comb product operation determine rainbow-vertex cycle complete...

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

We consider the problem of finding a cheapest Hamiltonian path of a complete graph satisfying a relaxed triangle inequality, i.e., such that for some parameter β > 1, the edge costs satisfy the inequality c({x, y}) ≤ β `

A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

For a connected graph, path containing all vertices is known as Hamiltonian path. general graphs, there no necessary and sufficient condition for the existence of paths complexity finding in graphs NP-Complete. We present 2-trees. Using our characterization, we also linear-time algorithm Our characterization based on deep understanding structure 2-trees combinatorics presented here may be used ...

The weight of a multicast shortest path tree in the complete graph with exponential link weights is expressed as a random variable. The new framework elegantly allows the computation of the average multicast weight.

We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian graphs. We analyse the mixing time of a Markov chain on the Eulerian orientations of a planar gra...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...