Average connectivity and average edge-connectivity in graphs

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Average connectivity and average edge-connectivity in graphs

Connectivity and edge-connectivity of a graph measure the difficulty of breaking the graph apart, but they are very much affected by local aspects like vertex degree. Average connectivity (and analogously, average edge-connectivity) has been introduced to give a more refined measure of the global “amount” of connectivity. In this paper, we prove a relationship between the average connectivity a...

متن کامل

Average Distance and Edge-Connectivity I

The average distance μ(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G. We prove that if G is a λ-edge-connected graph of order n, then the bounds μ(G) ≤ 2n/15 + 9, if λ = 5, 6, μ(G) ≤ n/9 + 10, if λ = 7 and μ(G) ≤ n/(λ + 1) + 5, if λ ≥ 8 hold. Our bounds are shown to be best possible and our results solve a problem of Plesńık [12].

متن کامل

Average distance and vertex-connectivity

The average distance μ(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G, i.e., μ(G) = ( n 2 )−1∑ {x,y}⊂V (G) dG(x, y), where V (G) denotes the vertex set of G and dG(x, y) is the distance between x and y. We prove that if G is a κ-vertex-connected graph, κ ≥ 3 an odd integer, of order n, then μ(G) ≤ n 2(κ+1) + O(1). Our bound is shown to be...

متن کامل

On the edge-connectivity of C_4-free graphs

Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...

متن کامل

Edge-connectivity and super edge-connectivity of P2-path graphs

For a graph G, the P2-path graph, P2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2013

ISSN: 0012-365X

DOI: 10.1016/j.disc.2013.05.024