The commuting graph \(\varDelta (G)\) of a finite non-abelian group G is a simple graph with vertex set G, and two distinct vertices x, y are adjacent if \(xy = yx\). In this paper, first we discuss some properties of \(\varDelta (G)\). We determine the edge connectivity and the minimum degree of \(\varDelta (G)\) and prove that both are equal. Then, other graph invariants, namely: matching number, clique number, boundary vertex, of \(\varDelta (G)\) are studied. Also, we give necessary and sufficient condition on the group G such that the interior and center of \(\varDelta (G)\) are equal. Further, we investigate the commuting graph of the semidihedral group \(SD_{8n}\). In this connection, we discuss various graph invariants of \(\varDelta (SD_{8n})\) including vertex connectivity, independence number, matching number and detour properties. We also obtain the Laplacian spectrum, metric dimension and resolving polynomial of \(\varDelta (SD_{8n})\).

有限的非阿贝尔群G的换向图\（\ varDelta（G）\）是具有顶点集G的简单图，如果\（xy = yx \），则两个不同的顶点x，  y相邻。在本文中，我们首先讨论\（\ varDelta（G）\）的一些属性。我们确定边缘连接性和\（\ varDelta（G）\）的最小程度，并证明两者相等。然后，研究其他图不变式，即：\（\ varDelta（G）\）的匹配数，集团数，边界顶点。另外，我们给G组赋予必要和充分的条件，使得G的内部和中心\（\ varDelta（G）\）相等。此外，我们研究了半二面体\（SD_ {8n} \）的换向图。在这方面，我们讨论\（\ varDelta（SD_ {8n}）\）的各种图形不变式，包括顶点连通性，独立性，匹配数和绕道属性。我们还获得\（\ varDelta（SD_ {8n}）\）的拉普拉斯谱，度量维和解析多项式。