7 citations · 22 across the 19 of their papers we have counts for
19 papers
The Sufficient Set of Congruences of Binomial Coefficients for Primality
Zubeyir Cinkir
For any given integer , we show that primality of is equivalent to congruences of binomial coefficients modulo . We also give extensi…
The Number of Spanning Trees for The Generalized Cones of , The Generalized Half Cones of and Some Family of Modified
Zubeyir Cinkir
We compute the total number of spanning trees for the generalized cone of the complete graph and a number of families of some modified bipartite graphs . In particul…
Explicit Rayleigh's Principles for Resistive Electrical Network and The Total Number of Spanning Trees of Graphs
Zubeyir Cinkir
We give identities for the voltage and resistance functions on a metrized graph to show how these functions behave under any edge deletion/contraction and the identification of any…
Beyond Wolstenholme's Theorem
Zubeyir Cinkir
Wolstenholme's type summations involve certain powers of all residues modulo some prime number . We first consider the sums of double or triple products of certain powers of…
An extension of Lucas Theorem
Zubeyir Cinkir, Aysegul Ozturkalan
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coeffici…
Effective Resistances and Kirchhoff index of Prism Graphs
Zubeyir Cinkir
We explicitly compute the effective resistances between any two vertices of a prism graph by using circuit reductions and our earlier findings on a ladder graph. As an application,…