‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

We show here a natural extension of finite graph automata, by allowing each node of a network to store in its memory some pieces of information that are only bounded by the size of the underlying network (like a unique address). Depending of the power of the new local transition function, we show results about the power of the global function computed by the graph automata. The main result is t...

The power domination problem is to find a minimum placement of phase measurement units (PMUs) for observing the whole electric power system represented by a graph G. The number of such a minimum placement of PMUs is called the power domination number of G and is denoted by γp(G). Finding γp(G) of an arbitrary graph is known to be NP-complete. In this paper, we deal with the power domination pro...

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

Abstract As the core part of electric ship, power battery system is fault-prone area whole ship due to harsh working environment and complex structure. This paper uses method based on directed graph model build ship’s with module as basic unit achieve fault location at level carries out simulation experiments prove feasibility scheme.