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math.CO2026

-Embeddability of Regular Quadrilateral Maps on the Torus and the Klein Bottle

Guangfu Wang, Wenchao Cong, Chunxiao Xu

A connected graph is called -embeddable if its shortest-path metric admits an isometric embedding into the -space; equivalently, in the finite case, it admits a sca…

math.CO2026

On the Lei--Bai conjecture on -regular Lin--Lu--Yau Ricci-flat graphs

Guangfu Wang, Wensheng Sun, Yujun Yang

We study the Ricci curvature introduced by Lin, Lu, and Yau. A graph is called Ricci-flat if every edge has curvature zero. Lei and Bai classified -regular symmetric Ricci-flat…

math.CO2026

Almost complete graphs determined by Laplacian hook immanantal polynomials

Shuaijun Li, Guangfu Wang

Let \(\mathscr{G}_n\) be the family of simple graphs obtained from \(K_n\) by deleting at most five edges. For a fixed integer \(1\leq k\leq n\), let \(Φ_k(L(G),x)\) denote the imm…

math.CO2026

Principal minors of effective-resistance matrices and local resistance radii

Guangfu Wang

Let be a finite connected weighted graph and let be its effective-resistance matrix. For every nonempty vertex set , we factor the cofactor sum and determinant of the pr…

math.CO2026

Root cubes and two-vertex deletions from daisy grids

Guangfu Wang

Daisy cubes are finite partial cubes that admit an isometric hypercube embedding whose labels form a Boolean down-set. Call a vertex a root if it can receive the all-zero label in…

math.CO2026

A complete classification of metrizable and strictly metrizable theta graphs

Guangfu Wang

Cizma and Linial asked for a classification of the metrizable theta graphs. We solve both their problem and its strict analogue. For , the theta graph is m…

math.CO2019

O-Fibonacci -cube as Cartesian products

Jianxin Wei, Guangfu Wang

Let and be positive integers. Then the O-Fibonacci -cube is the subgraph of induced on the binary words in which there is at least $p-1…

math.CO2019

On the Fibonacci -cubes

Jianxin Wei, Yujun Yang, Guangfu Wang

In this paper, first it is shown that the "FSibonacci -cube"(denoted as ) studied in many papers, such as \cite{OZY}, \cite{K1}, \cite{OZ}, \cite{KR} and \ci…