Let l > 0 be an integer, and G be a graph without loops. An l-link of G is a walk of length l in which consecutive edges are different. We identify an l-link with its reverse sequence. The l-link graph Ll(G) of G is defined to have vertices the l-links of G, such that two vertices of Ll(G) are adjacent if their corresponding l-links are the initial and final subsequences of an (l + 1)link of G....

Let $G$ be a finite group and $Gamma(G)$ the prime graph of $G$‎. ‎Recently people have been using prime graphs to study simple groups‎. ‎Naturally we pose a question‎: ‎can we use prime graphs to study almost‎ ‎simple groups or non-simple groups? In this paper some results in‎ ‎this respect are obtained and as follows‎: ‎$Gcong S_p$ if and only‎ ‎if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$‎, ‎whe...

Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...

Nowadays, one of the main problems encountered in minimally invasive surgery and telesurgery is the detection of arteries in tissue. In this study, for the first time, tactile detection of an artery in tissue and distinguishing it from the tumor has been modeled by finite element method. In this modeling, three 2D models of tissue have been created: tissue, tissue including a tumor, and tissue ...

A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finite-state automaton. The visual perception of the structure properties of automata is an important goal. A synchronizing word of a deterministic automaton is a word in the alphabet of colors of its edges ...

A distinguishing colouring of a graph is a colouring of the vertex set such that no non-trivial automorphism preserves the colouring. Tucker conjectured that if every non-trivial automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We show that the requirement of local finiteness is necessary by giving a nonlocally finite graph for w...