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- Klavdija Kutnar, Aleksander Malnic, Dragan Marusic, Stefko Miklavic
- Discrete Mathematics
- 2005

A graph $X$ is said to be {\it distance--balanced} if for any edge $uv$ of $X$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$. A graph… (More)

- István Kovács, Klavdija Kutnar, Dragan Marusic
- Journal of Graph Theory
- 2010

Given natural numbers n⩾3 and 1⩽a, r⩽n−1, the rose window graph Rn(a, r) is a quartic graph with vertex set… (More)

- Klavdija Kutnar, Dragan Marusic
- Discrete Applied Mathematics
- 2007

A graph is said to be cyclic $k$-edge-connected, if at least $k$ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of $k$ edges is called a… (More)

- Klavdija Kutnar, Dragan Marusic, Dave Witte Morris, Joy Morris, Primoz Sparl
- Ars Math. Contemp.
- 2010

We prove that if Cay(G;S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G;S) has a hamiltonian cycle. More precisely, if p, q, and r are… (More)

- Ademir Hujdurovic, Klavdija Kutnar, Dragan Marusic
- J. Comb. Theory, Ser. A
- 2014

Abstract A graph X is said to be G-half-arc-transitive if G ⩽ Aut ( X ) acts transitively on the set of vertices of X and on the set of edges of X but does not act transitively on the set of arcs of… (More)

- István Kovács, Klavdija Kutnar, János Ruff
- Discrete Mathematics
- 2010

Given natural numbers n>=3 and [email protected]?a,[email protected]?n-1, the rose window graph R"n(a,r) is a quartic graph with vertex set {x"i|[email protected]?Z"n}@?{y"i|[email protected]?Z"n}… (More)

- Ademir Hujdurovic, Klavdija Kutnar, Dragan Marusic
- Ars Math. Contemp.
- 2016

An automorphism of a graph is said to be even / odd if it acts on the set of vertices as an even/odd permutation. In this article we pose the problem of determining which vertex-transitive graphs… (More)

- Klavdija Kutnar, Stefko Miklavic
- Eur. J. Comb.
- 2014

A nonempty graph @C is called nicely distance-balanced, whenever there exists a positive integer @c"@C, such that for any two adjacent vertices u,v of @C there are exactly @c"@C vertices of @C which… (More)

- Ademir Hujdurovic, Klavdija Kutnar, Dragan Marusic
- Eur. J. Comb.
- 2015

Abstract The concept of generalized Cayley graphs was introduced by Marusic et al. (1992), where it was asked if there exists a vertex-transitive generalized Cayley graph which is not a Cayley graph.… (More)

- Klavdija Kutnar, Dragan Marusic
- Discrete Mathematics
- 2009

In this article current directions in solving Lovasz's problem about the existence of Hamilton cycles and paths in connected vertex-transitive graphs are given.