Salem numbers, Pisot numbers, Mahler measure, and graphs.
Schur complements of matrices with acyclic bipartite graphs.
Selberg's trace formula on the -regular tree and applications.
Selected Topics from the Theory of Graph Energy: Hypoenergetic Graph
Semidefinite functions on categories.
Semidefinite programming and combinatorial optimization.
Sensor Location Problem for a Multigraph
MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow...
Several results on chordal bipartite graphs
The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that,...
Sharp bounds for the sum of the squares of the degrees of a graph
Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs
Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained...
Sharp upper bounds on the spectral radius of the Laplacian matrix of graphs.
Sign patterns that allow eventual positivity.
Sign patterns that require eventual positivity or require eventual nonnegativity.
Sign patterns that require or allow power-positivity.
Signed graphs with at most three eigenvalues
We investigate signed graphs with just 2 or 3 distinct eigenvalues, mostly in the context of vertex-deleted subgraphs, the join of two signed graphs or association schemes.
Signless Laplacians and line graphs
Singular value inequality and graph energy change.
Singular values of tournament matrices.
Skew spectra of oriented graphs.
Small integral trees.