Graphs with prescribed maximal subgraphs and critical chromatic graphs
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Graphs with prescribed size and vertex parities
Philip J. Pratt, Donald W. Vanderjagt (1977)
Colloquium Mathematicae
Graphs with rainbow connection number two
Arnfried Kemnitz, Ingo Schiermeyer (2011)
Discussiones Mathematicae Graph Theory
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that rc(G) = 2 for every connected graph G of order n and size m, where . We also characterize graphs with rainbow connection number two and large clique number.
Graphs with smallest sum of squares of vertex degrees
Ivan Gutman (2003)
Kragujevac Journal of Mathematics
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