Abstract
AbstractIn this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs
Highlights
Let G = (V (G), E(G)) be a simple, finite and connected graph without loops
We present some interesting result of Lin et al [8]. They proved the lower and upper bound on the status of a connected unweighted graph G in terms of some spanning trees of G
We prove the lower and upper bound of double branch weight DBW (G) and give an algorithm for constructing quadrangular outerplanar graphs with some interesting properties
Summary
The centroid of T , denoted by C1(T ), is the set of vertices in T with the smallest branch weight. The second centroid of T , denoted by C2(T ), is the set of vertices in T with the second smallest branch weight. We present some interesting result of Lin et al [8] They proved the lower and upper bound on the status of a connected unweighted graph G in terms of some spanning trees of G. The double centroid of G, denoted by DC1(G), is the set of vertices in G with the smallest vertex double branch weight. The second double centroid of G, denoted by DC2(G), is the set of vertices in G with the second smallest vertex double branch weight.
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