The edge tenacity of a split graph

author

Bahareh Bafandeh Mayvan Department of Computer Engineering, Ferdowsi University of Mashhad

Abstract:

The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split graph with minimum vertex degree δ(G) we prove that if δ(G)≥|E(G)|/[|V(G)|-1] then its edge-tenacity is |E(G)|/[|V(G)|-1] .

Upgrade to premium to download articles

Already have an account?login

similar resources

the edge tenacity of a split graph

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

full text

THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

full text

On the tenacity of cycle permutation graph

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

full text

Edge-tenacity in Networks

Numerous networks as, for example, road networks, electrical networks and communication networks can be modeled by a graph. Many attempts have been made to determine how well such a network is "connected" or stated differently how much effort is required to break down communication in the system between at least some nodes. Two well-known measures that indicate how "reliable" a graph is are the...

full text

Towards a measure of vulnerability, tenacity of a Graph

If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.In this paper we discuss...

full text

On the Edge-Tenacity of Graphs

The edge-tenacity Te(G) of a graph G was defined as Te(G) = min F⊂E(G) {| F | +τ(G− F ) ω(G− F ) } where the minimum is taken over all edge cutset F of G. We define G-F to be the graph induced by the edges of E(G) − F , τ(G − F ) is the number of edges in the largest component of the graph induced by G-F and ω(G−F ) is the number of components of G− F . A set F ⊂ E(G) is said to be a Te-set of ...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}

Journal title

Journal of Algorithms and Computation

volume 47 issue 1

pages 119- 125

publication date 2016-05-01

unfollow

{@ msg @}

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Vertex degree split graphs edge tenacity

Hosted on Doprax cloud platform doprax.com