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The Gutman Index and the Edge-Wiener Index of Graphs with Given Vertex-Connectivity

Jaya Percival Mazorodze, Simon Mukwembi, Tomáš Vetrík (2016)

Discussiones Mathematicae Graph Theory

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 of given graph. In this paper we present asymptotically sharp upper bounds on the Gutman index and the edge-Wiener index for graphs of given order and vertex-connectivity κ, where κ is a constant. Our results substantially generalize and extend known results in the area.

The irregularity of graphs under graph operations

Hosam Abdo, Darko Dimitrov (2014)

Discussiones Mathematicae Graph Theory

The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and sym- metric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned...

The leafage of a chordal graph

In-Jen Lin, Terry A. McKee, Douglas B. West (1998)

Discussiones Mathematicae Graph Theory

The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n - lg n - 1/2 lg lg n + O(1). The proper leafage l*(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and lower bounds on l*(G). Leafage equals proper leafage on claw-free chordal graphs. We use asteroidal...

The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic

Yi Wang, Yi-Zheng Fan, Xiao-Xin Li, Fei-Fei Zhang (2015)

Discussiones Mathematicae Graph Theory

A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains...

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