Independence in Function Graphs
نویسندگان
چکیده
Given two graphs G and H and a function f ⊂ V (G) × V (H), Hedetniemi [9] defined the function graph GfH by V (GfH) = V (G)∪ V (H) and E(GfH) = E(G) ∪ E(H) ∪ {uv|v = f(u)}. Whenever G ∼= H, the function graph was called a functigraph by Chen, Ferrero, Gera and Yi [7]. A function graph is a generalization of the α-permutation graph introduced by Chartrand and Harary [5]. The independence number of a graph is the size of a largest set of mutually non-adjacent vertices. In this paper, we study independence number in function graphs. In particular, we give a lower bound in terms of the order and the chromatic number, which improves on some elementary results and has a number of interesting corollaries.
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