A bipartite biregular (m, n; g) (m,n;g)‐graph Γ Γ is a bipartite graph of even girth gg having
the degree set m, n {m,n\} and satisfying the additional property that the vertices in the same …

An $(\{r, m\}; g) $-graph is a (simple, undirected) graph of girth $ g\geq3 $ with vertices of
degrees $ r $ and $ m $ where $2\leq r< m $. Given $ r, m, g $, we seek the $(\{r, m\}; g) …

Abstract Let $2\leq k_1< k_2<\ldots< k_t $, $3\leq g_1< g_2<\ldots< g_s< N $ be integer
parameters. A $(k_1, k_2,\ldots, k_t; g_1, g_2,\dots, g_s; N) $-graph is a graph that contains …

A graph of girth g that contains vertices of degrees r and m is called a bi-regular ({r, m}, g)-
graph. As with the Cage Problem, we seek the smallest ({r, m}, g)-graphs for given …

Biregular‐cages are graphs of girth g that contain vertices of degrees r and m and are of the
smallest order among all such graphs. We show that for every and every odd, there exists an …

Given three positive integers r, m and g, one interesting question is the following: What is the
minimum number of vertices that a graph with prescribed degree set {r, m}, 2≤ r< m, and …

Let r, m, 2≤ r< m and g≥ 3 be three positive integers. A graph with a prescribed degree set
r, m and girth g having the least possible number of vertices is called a bi-regular cage or an …

An\emph {$(3, m; g) $ semicubic graph} is a graph in which all vertices have degrees either
$3 $ or $ m $ and fixed girth $ g $. In this paper, we construct families of semicubic graphs of …

In this paper, we obtain new lower and upper bounds for the problem of bipartite biregular
cages. Moreover, for girth 6, we give the exact parameters of the (m, n; 6)-bipartite biregular …

Let $2\le r< m $ and $ g $ be positive integers. An $({r, m}; g) $--graph}(or biregular graph) is
a graph with degree set ${r, m} $ and girth $ g $, and an $({r, m}; g) $-cage (or biregular …