Jernej Azarija

activity

20082016

most citedThere is no (95,40,12,20) strongly regular graph

2 citations · 2 across the 10 of their papers we have counts for

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Showing 2012 · math.COShow all

4 papers · 2 filters

math.CO2012

Moore graphs and cycles are extremal graphs for convex cycles

Jernej Azarija, Sandi Klavžar

Let $ρ (G)$ denote the number of convex cycles of a simple graph G of order n, size m, and girth 3 <= g <=n. It is proved that $ρ (G) \leq \frac{n}{g} (m - n + 1)$ and that equality holds…

math.CO2012

Sharp upper and lower bounds on the number of spanning trees in Cartesian product of graphs

Jernej Azarija

Let $G_{1}$ and $G_{2}$ be simple graphs and let $n_{1} = ∣ V (G_{1}) ∣$ , $m_{1} = ∣ E (G_{1}) ∣$ , $n_{2} = ∣ V (G_{2}) ∣$ and $m_{2} = ∣ E (G_{2}) ∣.$ In this paper we derive sharp upper and lower bounds for the…

math.CO2012

Counting graphs with different numbers of spanning trees through the counting of prime partitions

Jernej Azarija

Let A_n (n >= 1) be the set of all integers x such that there exists a connected graph on n vertices with precisely x spanning trees. In this paper, we show that |A_n| grows faster…

math.CO2012

Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees

Jernej Azarija, Riste Škrekovski

Let $α (n)$ be the least number $k$ for which there exists a simple graph with $k$ vertices having precisely $n \geq 3$ spanning trees. Similarly, define $β (n)$ as the least number…