نتایج جستجو برای: non connected graph
تعداد نتایج: 1581338 فیلتر نتایج به سال:
The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...
let r be a non-commutative ring with unity. the commuting graph of $r$ denoted by $gamma(r)$, is a graph with a vertex set $rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if $ab=ba$. in this paper, we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$. it is shown that, $gamma(r)$ is the disjoint ...
For a 2-factor F of a connected graph G, we consider G − F , which is the graph obtained from G by removing all the edges of F . If G − F is connected, F is said to be a non-separating 2-factor. In this paper we study a sufficient condition for a 2r -regular connected graph G to have such a 2-factor. As a result, we show that a 2r -regular connected graph G has a non-separating 2-factor wheneve...
a fullerene graph is a 3−connected planar graph whose faces are pentagons and hexagons.the clar number of a fullerene is the maximum size of sextet patterns, the sets of disjointhexagons which are all m-alternating for a kekulé structure m of f. an exact formula of clarnumber of some fullerene graphs and a class of carbon nanocones are obtained in this paper.
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
In this paper a finite-time flocking of multi-agent system with input saturation is investigated. By introducing a new control protocol, it is show that speed and position of agents with double-integrator dynamics converge to the speed and position of leader in finite time. It is assumed that the graph between the agents is connected and that at least one agent is informed of the leader speed a...
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
Given a graph G and a positive integer k, denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k. A graph G is called pseudo-k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo-k Hamiltonian-connec...
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