4 citations · 5 across the 14 of their papers we have counts for
6 papers · 1 filter
Beyond Bass Collapse: New Irregular Edge-Space Invariants in Ihara Theory
Hartosh Singh Bal
Let \(G\) be a finite simple graph and let \(T\) be its Hashimoto operator on the directed-edge space. We show that edge reversal induces a canonical symmetric/antisymmetric splitt…
The Antisymmetric Line Graph
Hartosh Singh Bal
Let be a finite simple graph with oriented incidence matrix . The signed graph on edge set with adjacency matrix \[ A_{\mathcal A(G)}=D^{\mathsf T}D-2I \] is classica…
Perfecting the Line Graph
Hartosh Singh Bal
We study the doubled edge-stage lift \[ \HL'_2(G)=L(G\otimes K_2), \] the line graph of the canonical bipartite double cover of a graph \(G\). The natural involution \((u,v)\leftri…
Completely Additive Height Functions: Profile Laws, Matula Bounds, and Inverse Growth
Hartosh Singh Bal
The height (H(n)) of an integer (n) is classically the number of iterations of Euler's totient function required to reach (1). H. N. Shapiro showed that a modification of this func…
Lognormal Degree Distribution in the Partition Graphs
Hartosh Singh Bal
We demonstrate a method for listing all ordinary partitions of n as binary words of length (n-1). The resulting family imbued with the hamming distance yields subgraphs of the Hamm…
Stanley--Elder--Fine theorems for colored partitions
Hartosh Singh Bal, Gaurav Bhatnagar
We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored parti…