Determination of the star valency of a graph

Authors:
Jinquan Dong;Yanpei Liu;Cun-Quan Zhang
Affiliations:
Department of Management, Inner Mongolia Polytechnic University, Huhhut 010062, People's Republic of China;Department of Mathematics, Northern Jiaotong University, Beijing 100044, People's Republic of China;Department of Mathematics, West Virginia University, Morgantown, WV
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

The star valency of a graph G is the minimum, over all star decompositions π, of the maximum number of elements in π incident with a vertex. The maximum average degree of G, denoted by dmax-ave(G), is the maximum average degree of all subgraphs of G. In this paper, we prove that the star valency of G is either ⌈dmax-ave(G)/2⌉ or ⌈dmax-ave(G)/2⌉ + 1, and provide a polynomial time algorithm for determining the star valency of a graph.