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Counting geodesic paths in graphs
Martin Knor, Jelena Sedlar, Riste Škrekovski +1
A geodesic is a shortest path which connects a pair of vertices of a graph G. In this paper we define the geodesic subpath number gpn(G) of a graph G as the number of geodesics in…
Proper Z4 x Z2-colorings: structural characterization with application to some snarks
Jelena Sedlar, Riste Škrekovski
A proper abelian coloring of a cubic graph G by a finite abelian group A is any proper edge-coloring of G by the non-zero elements of A such that the sum of the colors of the three…
Normal 5-edge coloring of some more snarks superpositioned by the Petersen graph
Jelena Sedlar, Riste Škrekovski
A normal 5-edge-coloring of a cubic graph is a coloring such that for every edge the number of distinct colors incident to its end-vertices is 3 or 5 (and not 4). The well known Pe…
Resolving vertices of graphs with differences
Iztok Peterina, Jelena Sedlar, Riste Škrekovski +1
The classical (vertex) metric dimension of a graph G is defined as the cardinality of a smallest set S in V (G) such that any two vertices x and y from G have different distances t…
Normal 5-edge-coloring of some snarks superpositioned by Flower snarks
Jelena Sedlar, Riste Škrekovski
An edge e is normal in a proper edge-coloring of a cubic graph G if the number of distinct colors on four edges incident to e is 2 or 4: A normal edge-coloring of G is a proper edg…
Normal 5-edge-coloring of some snarks superpositioned by the Petersen graph
Jelena Sedlar, Riste Škrekovski
In a (proper) edge-coloring of a bridgeless cubic graph G an edge e is rich (resp. poor) if the number of colors of all edges incident to end-vertices of e is 5 (resp. 3). An edge-…