Now showing items 1-6 of 6
The Gutman Index and the Edge-Wiener Index of Graphs with given Vertex-Connectivity
(University of Zielona Góra, 2015-12-30)
The Gutman index and the edge-Wiener index have been extensively investigated particularly in the last decade. An important stream of re- search on graph indices is to bound indices in terms of the order and other parameters ...
Upper Bounds on the Diameter of Bipartite and Triangle-Free Graphs with Prescribed Edge Connectivity
Graph theory is used to study the mathematical structures of pairwise relations among objects. Mathematically, a pair G=(V,E) is a crisp graph, where V is a nonempty set and E is a relation on V. -e order of a graph G ...
Spanning paths in graphs
The Conjecture, Graffiti.pc 190, of the computer program Graffiti.pc, instructed by DeLavi˜na, state that every simple connected graph G with minimum degree δ and leaf number L(G) such that δ ≥ 1 2 (L(G) + 1), is traceable. ...
An Upper Bound on the Radius of a 3-Vertex-Connected C4-Free Graph
Let G=(V,E) be a finite, connected, undirected graph with vertex set V and edge set E. -e distance dG (u,v) between two vertices u, v of G is the length of a shortest u-v path in G.-e eccentricity ec(v)of a vertex v∈V is ...
Average distance and edge-connectivity I
(Society for Industrial and Applied Mathematics, 2015-01-15)
The average distance $\mu(G)$ 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 $\lambda$-edge-connected graph of order n, then the bounds $\mu(G) ...
Minimum degree, leaf number and traceability
(Institute of Mathematics of the Czech Academy of Sciences, 2013-03-26)
Let G be a finite connected graph with minimum degree δ. The leaf number L (G) of G is defined as the maximum number of leaf vertices contained in a spanning tree of G. We prove that if δ >12(L (G) + 1), then G is 2-connected. ...