AbstractLet σk(G) denote the number of cycles of length k in a graph G. In this paper, we first prove that if G and H are χ-equivalent graphs, then σk(G) = σk(H) for all k with g⩽k⩽32g − 2, w ere g is the girth of G. This result will then be incorporated with a structural theorem obtained in [7] to show that all uniform subdivisions of some families of graphs, including the complete bipartite graphs and certain cages, are χ-unique
AbstractFor a graph G, let P(G,λ) be its chromatic polynomial and let [G] be the set of graphs havin...
AbstractThis paper is partitioned into two parts. In the first part we determine the maximum number ...
AbstractLet K(p, q), p ⩽ q, denote the complete bipartite graph in which the two partite sets consis...
AbstractLet σk(G) denote the number of cycles of length k in a graph G. In this paper, we first prov...
AbstractLet P(G;λ) denote the chromatic polynomial of a graph G. G is chromatically unique if G is i...
AbstractLet P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically ...
AbstractLet K(p, q), p ⩽ q, denote the complete bipartite graph in which the two partite sets consis...
AbstractIn this note, it is shown that all graphs Fn,k for odd integer n ⩾ 5, and integer k ⩾ 1 are ...
AbstractWe prove the chromatic uniqueness of the following infinite families of bipartite graphs: Km...
AbstractA graph is said to be chromatically unique (or χ-unique) if it is uniquely determined by its...
Let \(P(G, x)\) be a chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are called ch...
Let P(G,x) be a chromatic polynomial of a graph G. Two graphs G and H are called chromatically equiv...
AbstractA graph is said to be chromatically unique (or χ-unique) if it is uniquely determined by its...
AbstractWe prove that graphs obtained from complete equibipartite graphs by deleting some independen...
AbstractLet W(n, m) denote the graph of order n obtained from the wheel Wn be deleting all but m con...
AbstractFor a graph G, let P(G,λ) be its chromatic polynomial and let [G] be the set of graphs havin...
AbstractThis paper is partitioned into two parts. In the first part we determine the maximum number ...
AbstractLet K(p, q), p ⩽ q, denote the complete bipartite graph in which the two partite sets consis...
AbstractLet σk(G) denote the number of cycles of length k in a graph G. In this paper, we first prov...
AbstractLet P(G;λ) denote the chromatic polynomial of a graph G. G is chromatically unique if G is i...
AbstractLet P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically ...
AbstractLet K(p, q), p ⩽ q, denote the complete bipartite graph in which the two partite sets consis...
AbstractIn this note, it is shown that all graphs Fn,k for odd integer n ⩾ 5, and integer k ⩾ 1 are ...
AbstractWe prove the chromatic uniqueness of the following infinite families of bipartite graphs: Km...
AbstractA graph is said to be chromatically unique (or χ-unique) if it is uniquely determined by its...
Let \(P(G, x)\) be a chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are called ch...
Let P(G,x) be a chromatic polynomial of a graph G. Two graphs G and H are called chromatically equiv...
AbstractA graph is said to be chromatically unique (or χ-unique) if it is uniquely determined by its...
AbstractWe prove that graphs obtained from complete equibipartite graphs by deleting some independen...
AbstractLet W(n, m) denote the graph of order n obtained from the wheel Wn be deleting all but m con...
AbstractFor a graph G, let P(G,λ) be its chromatic polynomial and let [G] be the set of graphs havin...
AbstractThis paper is partitioned into two parts. In the first part we determine the maximum number ...
AbstractLet K(p, q), p ⩽ q, denote the complete bipartite graph in which the two partite sets consis...
DOI
Add to ORKG