5 papers · 1 filter
The Goldman-Rota identity and the Grassmann scheme
Murali K. Srinivasan
We inductively construct an explicit (common) orthogonal eigenbasis for the elements of the Bose-Mesner algebra of the Grassmann scheme. The main step is a constructive, linear alg…
Counting spanning trees of the hypercube and its -analogs by explicit block diagonalization
Murali K. Srinivasan
The number of spanning trees of a graph is called the {\em complexity} of and is denoted . Let C(n) denote the {\em (binary) hypercube} of dimension . A classical…
The polytope of degree partitions
Amitava Bhattacharya, S. Sivasubramanian, Murali K. Srinivasan
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the conve…
Alternating Reachability
Amitava Bhattacharya, Uri N. Peled, Murali K. Srinivasan
We consider a graph with colored edges. A trail (vertices may repeat but not edges) is called \emph{alternating} when successive edges have different colors. Given a set of vertice…
Cones of closed alternating walks and trails
Amitava Bhattacharya, Uri N. Peled, Murali K. Srinivasan
Consider a graph whose edges have been colored red and blue. Assign a nonnegative real weight to every edge so that at every vertex, the sum of the weights of the incident red edge…