Let G be an n-vertex (n ≥ 3) simple graph embeddable on a surface of Euler genus. In this paper, we present upper bounds for the signless Laplacian spectral radius of planar graphs, outerplanar graphs and Halin graphs, respectively, in terms of order and maximum degree.
In this paper, we use the indirect sum construction (proposed by Carlet in 2004) for constructing the bent-negabent functions that are not provably contained in the Maiorana-McFarland class, which is the first significant attempt in this direction.
The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv| ≤ 2^4 x 3^6 or 2 x |Gv| x log2(|Gv|/2) ≤ |VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.